Write the general form of the antiderivative of f(x)=4x-2x^2+x*Sqrt(x) + e^x.
Hence calculate integral of 0 to 1 for the above equation
Hello,
Note that $\displaystyle \sqrt{x}=x^{1/2}$
Hence $\displaystyle x*\sqrt{x}=x^{3/2}$
Now here are a few points to help you find the antiderivative :
- an antiderivative for $\displaystyle x^n$ is $\displaystyle \frac{x^{n+1}}{n+1}$
- an antiderivative of a sum is the sum of the antiderivatives
- an antiderivative of $\displaystyle e^x$ is $\displaystyle e^x$
- don't forget the integration constant.
Let F be the antiderivative you've found.hence calculate integral of 0 to 1 for the above equation
The integral from 0 to 1 is defined as follows :
$\displaystyle \int_0^1 f(x) ~ dx=F(1)-F(0)$