Integration Practice

Calculus Level 3

0 π x 7 sin x d x \int_{0}^{\pi} x^7 \sin x \ \mathrm{d}x


The answer is 379.1119.

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2 solutions

Chua Hsuan
Feb 14, 2021

Reduction formula

Vaibhav Vinayaka
Sep 18, 2018

I used wolframalpha

@Aryan Sanghi , how can I do this?

Vinayak Srivastava - 11 months ago

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See, there is a formula

f ( x ) . g ( x ) d x = f ( x ) g ( x ) d x ( d d x f ( x ) . g ( x ) d x ) d x \int f(x).g(x)dx = f(x)\int g(x)dx - \int\bigg(\frac{d}{dx}f(x) . \int g(x)dx\bigg)dx

Solve using above formula recursively and you'll get the answer. :)

Aryan Sanghi - 11 months ago

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Do I really need to study calculus or I can study only basics?

Vinayak Srivastava - 11 months ago

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@Vinayak Srivastava Even I know just basics.😂 Calculus isn't needed in detail till 1 2 t h 12^{th} . Basics are sufficient.

Aryan Sanghi - 11 months ago

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@Aryan Sanghi Ok, so I won't open calculus problems till 12th :)

Vinayak Srivastava - 11 months ago

@Aryan Sanghi I tried solving one or two steps, then it is repeating and I don't want to do so much work. But thanks for the formula. Maybe(rarely the case, actually) I'll remember it! :)

Vinayak Srivastava - 11 months ago

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