積分計算機 - Symbolab

Integral Calculator You can see your coupon in the user page Go To QuillBot Upgrade to Pro Continue to site We've updated our Privacy Policy effective December 15. Please read our updated Privacy Policy and tap Continue Solutions Integral Calculator Derivative Calculator Algebra Calculator Matrix Calculator More... Graphing Line Graph Calculator Exponential Graph Calculator Quadratic Graph Calculator Sine Graph Calculator More... Calculators BMI Calculator Compound Interest Calculator Percentage Calculator Acceleration Calculator More... Geometry Pythagorean Theorem Calculator Circle Area Calculator Isosceles Triangle Calculator Triangles Calculator More... AI Chat Tools Notebook Groups Cheat Sheets Worksheets Study Guides Practice Verify Solution en English Español Português Français Deutsch Italiano Русский 中文(简体) 한국어 日本語 Tiếng Việt עברית العربية Upgrade Close Accept Terms Good job! Practice More Type your Answer Verify x^2 x^{\msquare} \log_{\msquare} \sqrt{\square} \nthroot[\msquare]{\square} \le \ge \frac{\msquare}{\msquare} \cdot \div x^{\circ} \pi \left(\square\right)^{'} \frac{d}{dx} \frac{\partial}{\partial x} \int \int_{\msquare}^{\msquare} \lim \sum \infty \theta (f\:\circ\:g) f(x) ▭\:\longdivision{▭} \times \twostack{▭}{▭} + \twostack{▭}{▭} - \twostack{▭}{▭} \left( \right) \times \square\frac{\square}{\square} Take a challenge Subscribe to verify your answer Subscribe Are you sure you want to leave this Challenge? By closing this window you will lose this challenge Cancel Leave Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Number Line Expanded Form Mean, Median & Mode Algebra Equations Inequalities System of Equations System of Inequalities Testing Solutions Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Interval Notation Pi (Product) Notation Induction Prove That Logical Sets Word Problems Pre Calculus Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Trigonometry Calculus Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Fourier Transform Functions Line Equations Functions Arithmetic & Comp. Conic Sections Transformation Linear Algebra Matrices Vectors Trigonometry Quadrant Coterminal Angle Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify Statistics Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution Physics Mechanics Chemistry Chemical Reactions Chemical Properties Finance Simple Interest Compound Interest Present Value Future Value Economics Point of Diminishing Return Conversions Currency Roman Numerals Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Degrees Minutes Seconds Hexadecimal Scientific Notation Distance Weight Time Volume Special Offer Double the Tools. One Smart Bundle. to master your math and writing! Pro Full access to solution steps Full access to AI chat Practice and improve Access from any device No ads Unlimited storage Detect AI-generated content Advanced Grammar Checker AI Humanizer Paraphrase in unlimited modes Summarize any text Much More! Restrictions apply, check out our FAQs. Go back Purchase Bundle Back to School Promotion Annual Annual - $ % OFF Annual plan One time offer for one year, then $ Go back + qb-banner-title Solutions > Calculus Calculator > Integral Calculator Topic Pre Algebra Algebra Pre Calculus Calculus Derivatives First Derivative WRT Specify Method Chain Rule Product Rule Quotient Rule Sum/Diff Rule Second Derivative Third Derivative Higher Order Derivatives Derivative at a point Partial Derivative Implicit Derivative Second Implicit Derivative Derivative using Definition Derivative Applications Tangent Slope of Tangent Normal Curved Line Slope Extreme Points Tangent to Conic Linear Approximation Difference Quotient Horizontal Tangent Limits One Variable Multi Variable Limit One Sided At Infinity Specify Method L'Hopital's Rule Squeeze Theorem Chain Rule Factoring Substitution Sandwich Theorem Integrals Indefinite Integrals Definite Integrals Specific-Method Partial Fractions U-Substitution Trigonometric Substitution Weierstrass Substitution By Parts Long Division Improper Integrals Antiderivatives Double Integrals Triple Integrals Multiple Integrals Integral Applications Limit of Sum Area under curve Area between curves Area under polar curve Volume of solid of revolution Arc Length Function Average Integral Approximation Riemann Sum Trapezoidal Simpson's Rule Midpoint Rule Series Convergence Geometric Series Test Telescoping Series Test Alternating Series Test P Series Test Divergence Test Ratio Test Root Test Comparison Test Limit Comparison Test Integral Test Absolute Convergence Power Series Radius of Convergence Interval of Convergence ODE Linear First Order Linear w/constant coefficients Separable Bernoulli Exact Second Order Homogenous Non Homogenous Substitution System of ODEs IVP using Laplace Series Solutions Method of Frobenius Gamma Function Multivariable Calculus Partial Derivative Implicit Derivative Tangent to Conic Multi Variable Limit Multiple Integrals Gradient Divergence Extreme Points Laplace Transform Inverse Taylor/Maclaurin Series Taylor Series Maclaurin Series Fourier Series Fourier Transform Functions Linear Algebra Trigonometry Statistics Physics Chemistry Finance Economics Conversions Add to Chrome Get our extension, you can capture any math problem from any website Full pad x^2 x^{\msquare} \log_{\msquare} \sqrt{\square} \nthroot[\msquare]{\square} \le \ge \frac{\msquare}{\msquare} \cdot \div x^{\circ} \pi \left(\square\right)^{'} \frac{d}{dx} \frac{\partial}{\partial x} \int \int_{\msquare}^{\msquare} \lim \sum \infty \theta (f\:\circ\:g) f(x) - \twostack{▭}{▭} \lt 7 8 9 \div AC + \twostack{▭}{▭} \gt 4 5 6 \times \square\frac{\square}{\square} \times \twostack{▭}{▭} \left( 1 2 3 - x ▭\:\longdivision{▭} \right) . 0 = + y \mathrm{partial\:fractions} \mathrm{substitution} \mathrm{long\:division} \mathrm{trigonometric\:substitution} \mathrm{by\:parts} See All area asymptotes critical points derivative domain eigenvalues eigenvectors expand extreme points factor implicit derivative inflection points intercepts inverse laplace inverse laplace partial fractions range slope simplify solve for tangent taylor vertex geometric test alternating test telescoping test pseries test root test Go Steps Graph Related Examples Generated by AI AI explanations are generated using OpenAI technology. AI generated content may present inaccurate or offensive content that does not represent Symbolab's view. Verify your Answer Subscribe to verify your answer Subscribe Save to Notebook! Sign in to save notes Sign in Verify Save Show Steps Hide Steps Number Line Related Integral Examples \int e^x\cos(x)dx \int \cos^3(x)\sin (x)dx \int \frac{2x+1}{(x+5)^3} \int_{0}^{\pi}\sin(x)dx \int_{a}^{b} x^2dx \int_{0}^{2\pi}\cos^2(\theta)d\theta partial\:fractions\:\int_{0}^{1} \frac{32}{x^{2}-64}dx substitution\:\int\frac{e^{x}}{e^{x}+e^{-x}}dx,\:u=e^{x} Show More Introduction to Integration What is an Integration? Integration is the union of elements to create a whole. Integral calculus allows us to find a function whose differential is provided, so integrating is the inverse of differentiating. It defines and computes the area of a region constrained by the graph of a function . Integration developed historically from the process of exhaustion, in which inscribing polygons approximated the area of a curved form. We distinguish integration into two forms: definite and indefinite integrals . Fundamental instruments in calculus , differentiation and integration have extensive use in mathematics and physics. Leibniz created the ideas of integration. Let us investigate integration, its features, and some of its effective approaches. Integration - An Inverse Process of Differentiation Integration is the opposite of differentiation basically. Integration helps us to determine the original function of a derivative if provided one. If $\frac{d(F(x))}{dx}=f(x)$, then $\int f(x)dx=F(x)+C$ . This is known as indefinite integrals. For Example Suppose $f(x)=x^3$ The derivative of f(x) is $f'(x)=3x^2$ The antiderivative of $3x^2$ is $x^3$ So the derivative of any constant is zero and anti-derivative of any expression will contain arbitrary constant denoted by C that is $ \int 3x^2dx=x^3+C$ Therefore, if $\frac{dy}{dx}=f(x)$, then we can write it as y = $\int f(x)dx=F(x)+C$ where: $\int f(x)dx$ will represent the complete class of integral. C is an arbitrary constant. x is the variable of equation. The symbol $\int$ denotes the integral. f(x) is the integrand. Rules of Integration Sum and Difference Rules: $\int [f(x) + g(x)] dx = \int f(x) dx + \int g(x) dx$ $\int [f(x) - g(x)] dx = \int f(x) dx - \int g(x) dx$ For example: $\int (x^2 + 3x) dx = \int x^2 dx + \int 3x dx$ $= \frac{x^3}{3} + \frac{3x^2}{2} + C$ Power Rule: $ \int x^ndx= \frac {x^{(n+1)}}{n+1} +C $ Please note here n$\neq$-1 For example: $\int x^5dx=\frac{x^6}{6}+C$ Exponential Rules: $ \int e^xdx=e^x+C$ $ \int a^xdx= \frac{a^x}{ln(a)}+C$ $ \int ln(x)dx=xln(x)-x+C$ Constant Multiplication Rule: $ \int adx=ax+C $ Reciprocal Rule: $ \int \frac{1}{x}dx=ln|x|+C $ Properties of Integration Properties of indefinite $\int [f(x) \pm g(x)]dx= \int f(x)dx \pm \int g(x)dx $ $ \int kf(x)dx = k \int f(x)dx $ (here k is the constant