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Integration Help needed

Hi all, can anyone help with integrating. It's the power of 1/2 that confusing me.

F(x) = 2x + 3x^1/2 , where x = 1 and x=4.

^Thanks

Reply 1

Indeterminate

Original post by Flutegirl02

Hi all, can anyone help with integrating. It's the power of 1/2 that confusing me.

F(x) = 2x + 3x^1/2 , where x = 1 and x=4.

^Thanks

Integrate term-wise, making use of the fact that

\displaystyle \int x^n \ dx = \dfrac{x^{n+1}}{n+1} + C

Reply 2

KyleBroflovski

Don't worry about the 1/2, just rewrite it as 0.5, so you've got 2x + 3x^0.5, now we know that we add 1 to the power and divide by that number in integration. So it becomes (2x^2)/2 + (3x^1.5)/1.5, this simplifies to x^2+2x^1.5, now go ahead and solve for those limits of 1 and 4. Don't add C to the end because this is definite integration.

Edit: Just want to clarify there is always C at the end, but since the integration is not indefinite the C gets cancelled out, +C - C = 0