It is the function that reverses what the derivative does. One function has many antiderivatives, but they all take the form of a function plus an arbitrary constant. Examples: Derivative of cos 2x and the derivative of sin 2x Definite Integral Example 1 Definite Integral Example 2...
Solution: Assume x2 = u ⇒ 2x dx = du. Substitute this into the integral, we have∫2x cos (x2) dx = ∫cos u du= sin u + C= sin (x2) + CAntiderivative Product RuleThe antiderivative product rule is also commonly called the integration by parts method of integration. It is ...
Question: Find the antiderivative of {eq}\int_{1}^{3}x^2dx {/eq} Integration: Consider a function {eq}\displaystyle f(x) {/eq} with upper limit {eq}\displaystyle b {/eq} and lower limit {eq}\displaystyle a {/eq} Then integral is written as {eq}\displaystyle \int _a^b f(x)...
Find the antiderivative of: 1) \int {\sin x}{(\cos x- \cos x \sin^2x)} \, dx 2) \int \cos^2x(1+\sin^2x) \, dx Find the antiderivative F(x) of f(x) = \sqrt[3]x given that F(0) = -1 Find the antiderivative F(x) of f(x) = \sqrt[3]x given F(0) = -1 ...
Integrate \frac {e^x}{(1+e^{(2x)})} What is the antiderivative of: \frac{\sin(2x)}{25+\cos^{2}(x)} What is the antiderivative of (2e^-x)^2? What is the antiderivative of f(x) = x^4 - 2\sqrt x + \frac{3}{x^3}?
f(x) = x 1/3/x 2/3 Find the antiderivative of: 1) \int {\sin x}{(\cos x- \cos x \sin^2x)} \, dx 2) \int \cos^2x(1+\sin^2x) \, dx Find the antiderivative of f ( x ) = x 3 ? 10 . Find the antiderivative of f(x) = (x^5 - x^3 + 6x)/(x...
Find the Antiderivative of f(x) = \frac{8 - 5x^4 + 3x^7}{x^7}. Find the antiderivative: dy/dx = x - e^x. Find the antiderivative of: 1) \int {\sin x}{(\cos x- \cos x \sin^2x)} \, dx 2) \int \cos^2x(1+\sin^2x) \, dx Find the antiderivative. f(x) = 4...
\int \left( x+ \frac {1}{x}-\sin (x) \right ) dxFind the following antiderivatives: a) \int x^6 dx b) \int x^\frac{-1}{2} dx c) \int (2x^5 - \frac{3}{x^5}) dxDetermine the following antiderivative: int (3 x + 5 x 5 2)dx...
f(x)=2x2+x+6x,f(1)=3 Antiderivatives: The indefinite integrals, also known as the antiderivatives came into existence in the1700s. They are just the reverse of the derivatives. We usually see the applications of the antiderivatives while evaluating the definite integrals becau...
Find the area of the region bounded by the curves y=sin−1(x6), y=0, and x=6 obtained by integrating with respect to y. Include the definite integral and the antiderivative. Area Between Functions: Given...