general form

**Faz** · December 15th 2008, 12:32 AM

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

**Moo** · December 15th 2008, 01:51 AM

Hello,

Originally Posted by Faz

write the general form of the antiderivative of f(x)=4x-2x^2+x*Sqrt(x) + e^x

Note that $\sqrt{x}=x^{1/2}$
Hence $x*\sqrt{x}=x^{3/2}$

Now here are a few points to help you find the antiderivative :
- an antiderivative for $x^n$ is $\frac{x^{n+1}}{n+1}$
- an antiderivative of a sum is the sum of the antiderivatives
- an antiderivative of $e^x$ is $e^x$
- don't forget the integration constant.

hence calculate integral of 0 to 1 for the above equation

Let F be the antiderivative you've found.

The integral from 0 to 1 is defined as follows :
$\int_0^1 f(x) ~ dx=F(1)-F(0)$

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