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Integration problem?

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(edited 8 years ago)
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Original post by MrPenguinPerson
Hello, so my maths teacher sets us this homework involving two integration questions that we haven't actually been taught how to do... I've given them a go but can't figure them out.

1. Differentiate (sinx)^5 and hence find the indefinite integral of (sinx)^4 dx
2. Differentiate (x^2 + 3)^4 and hence find the indefinite integral of (x^2 + 3)^3 dx

I am guessing it has something to do with reverse chain rule, but I am not completely sure. The rest of the internet has not helped, I would definitely appreciate some guidance.


Should the first one read: sin4(x)cos(x) dx\displaystyle\int \sin^4(x)\cos(x) \ dx?
As for what you need to do, you should differentiate the given function, and observe that the derivative is in fact a multiple of the indefinite integral.

Then you apply the Fundamental Theorem of Calculus don't worry if you don't know what that is: Essentially, if:
f(x) dx=F(x)\displaystyle\int f(x) \ dx =F(x) then f(x)=F(x)f(x)=F'(x)

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