Verify that F(x)=xln(x)−x is an antiderivative of ln(x). Proof of Anti-Derivative and By Parts Method: To prove the value of the anti-derivative of an integrand, we can apply the by parts method using the ILATE (inverse, logarithmic, algebraic, trigonometric, exp...
An antiderivative of function f(x) is a function whose derivative is equal to f(x). Is integral the same as antiderivative? The set of all antiderivatives of a function is the indefinite integral of the function. The difference between any two functions in the set is a constant. ...
1. Find the antiderivative of f(x) = x^2 + cos x . 2. Evaluate \lmoustache \sqrt{1-x^3} \ x^2 dx. Find the antiderivative of the function f(x) = tan^2(x) + (2x - 3)^5. Find an antiderivative for the function f(x) = \dfrac{1...
The function( F(x)) can be found by finding the indefinite integral of the derivative( f(x)). ( F(x)=∫ f(x)dx) Set up the integral to solve. ( F(x)=∫ (ln)(x)dxdx) Since ( d) is constant with respect to ( x), move ( d) out of the integral. ( d∫ (ln)(x)...
What is the antiderivative of \frac{3x}{x^2}? Find the most general antiderivative. \int ( \frac { 8 } { \sqrt { 1 - x ^ { 2 } } } - \frac { 5 } { x } ) d x Find the indefinite integral.\int \frac{ \ln5x}{x} dx ...
Properties of natural logs. Derivative of Natural Log dydx=ddxln(x). To find the derivative ofln(x), let's start with the following expression: y=ln(x) ey=x ddxey=ddxx ddxey=eydydx ddxx=1 eydydx=1 Solving fordydxgives us ...
Consider the functionf(x)=x2−1x2+1,wherex∈R.At what value ofxdoesf(x)attain minimum value? What is the minimum value off(x)? View Solution Free Ncert Solutions English Medium NCERT Solutions NCERT Solutions for Class 12 English Medium ...
The function f(x)=(3x−1)2sinx⋅ln(1+x),x≠0, is continuous at x=0, Then the value of f(0) is View Solution The function f(x)=(3x−1)2sinx⋅ln(1+x),x≠0, is continuous at x=0, Then the value of f(0) is View Solution Consider the function f(x)=x2−1x2...
What is the general antiderivative of \int \left(x^9 + 9^x\right)\,dx? (a) 9x^8 + \ln(9)9^x + C (b) 9x^{10} + \ln(9)9^x + C (c) \frac{1}{10}x^{10} + \frac{1}{\ln(9)}9^x + C (d) \frac{1}{10}x^{10} + 9^x + C What is the ant...
sec(x)tan(x)? Show all the steps. Antiderivative:In calculus, the term antiderivative denotes indefinite integration since the differentiation and integration are opposed to each other. It is also called antidifferentiation or inverse derivative, which means the inverse of derivative (i...