Integration of an algebraic and trigonometrical function

[Arkavo]

Homework Statement

x
∫((x^n)sinx)dx=0.75($\pi$^2-8) find n if n is a single digit positive integer
0

Homework Equations

∫uv.dx=u∫v.dx-∫(u'.∫v.dx).dx

The Attempt at a Solution

i tried putting n=1 or 2 but didnt get the result
i somehow don't think that's the method
help please

 

[Saitama]

Homework Statement

x
∫((x^n)sinx)dx=0.75($\pi$^2-8) find n if n is a single digit positive integer
0

Homework Equations

∫uv.dx=u∫v.dx-∫(u'.∫v.dx).dx

The Attempt at a Solution

i tried putting n=1 or 2 but didnt get the result
i somehow don't think that's the method
help please

Hi Arkavo!

Are you sure about the integration limits? Can you please recheck the question?

 

[Arkavo]

ok no the x is replaced by pi/2
sorry

 

[Ray Vickson]

Homework Statement

x
∫((x^n)sinx)dx=0.75($\pi$^2-8) find n if n is a single digit positive integer
0

Homework Equations

∫uv.dx=u∫v.dx-∫(u'.∫v.dx).dx

The Attempt at a Solution

i tried putting n=1 or 2 but didnt get the result
i somehow don't think that's the method
help please

You need to show your work (as required by PF rules); but first, you need to clarify your question. Do you mean that you want to solve the equation
$$\int_0^x t^n \sin(t) \, dt = \frac{3}{4} \left( \pi^2 - 8 \right)$$
to find x? Different small integer values of n give different solutions x, so you need to spell out in more detail what you want.

What was the value of your integral for n = 1 and for n = 2?

 

[Norules]

n=3

NR