SOLUTION: Hi all, I was hoping someone could show me how to find: the indefinite intergral of f (x) = 5x - 3x^2 + xsqrt(x) + 7 e^x and Hence calculate: 0∫2 (5x-3x^2 + xsqrt(x) + 7e

Algebra ->  Equations -> SOLUTION: Hi all, I was hoping someone could show me how to find: the indefinite intergral of f (x) = 5x - 3x^2 + xsqrt(x) + 7 e^x and Hence calculate: 0∫2 (5x-3x^2 + xsqrt(x) + 7e      Log On


   

Question 210007: Hi all, I was hoping someone could show me how to find:
the indefinite intergral of f (x) = 5x - 3x^2 + xsqrt(x) + 7 e^x
and Hence calculate: 0∫2 (5x-3x^2 + xsqrt(x) + 7e^x)dx
(The zero should be beneath the 2, but I dont know how to fix the input)
Any help would be great.
-Nick.
Answer by algebrapro18(249) About Me  (Show Source):
You can put this solution on YOUR website!
This is actually a definate integral if it has the bounds on it. First off I would start by simplifying xsqrt(x).

xsqrt%28x%29+=+x%2Ax%5E%281%2F2%29+=+x%5E%283%2F2%29

so this becomes ∫ %285x-3x%5E2+%2B+x%5E%283%2F2%29+%2B+7e%5Ex%29dx

*NOTE* I know this is a definite integral but I will leave the bounds off and then evaluate on the end, just because I can't get the bounds on the integral to come out either.

Now we just break it up piece by piece and this becomes

5∫x dx - 3∫x%5E2 dx + ∫ ) + 7(e^x)

Now we plug in the 2 and the 0 and in the first 3 terms the 0 doesn't matter
5(1/2(2)^2) - 3(1/3(2)^3) + 2/5(%282%29%5E5%2F2) + 7(e^2-e^0)
5(1/2(4)) - 3(1/3(8)) + 2/5(%2832%29%5E1%2F2) + 7(e^2-1)
5(2) - 8 + 2/5(%2832%29%5E1%2F2) + 7e^2-7
2 + 2/5(%2832%29%5E1%2F2) + 7e^2-7
-5 + 2/5(%2832%29%5E1%2F2) + 7e^2

I will leave you to plug that into your calculator and get the answer.