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.Com
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) (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).
so this becomes ∫
*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∫ 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() + 7(e^2-e^0)
5(1/2(4)) - 3(1/3(8)) + 2/5() + 7(e^2-1)
5(2) - 8 + 2/5() + 7e^2-7
2 + 2/5() + 7e^2-7
-5 + 2/5() + 7e^2
I will leave you to plug that into your calculator and get the answer.
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