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

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- Dec 15th 2008, 12:32 AMFaz
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 - Dec 15th 2008, 01:51 AMMoo
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.

Quote:

hence calculate integral of 0 to 1 for the above equation

The integral from 0 to 1 is defined as follows :

$\displaystyle \int_0^1 f(x) ~ dx=F(1)-F(0)$