Pure Mathematics

In=∫ x^nSinx dx....with the limits π/2 and 0
i found that In would be equal to n(π/2)^(n-1) -n(n-1) In-2
how do i deduce the value of I4? where n=4

1. 👍 0
2. 👎 0
3. 👁 598
1. you need to do integration by parts.

∫x^4 sinx dx
u=x^4
du = 4x^3 dx

dv = sinx dx
v = -cosx

∫x^4 sinx = -x^4 cosx + 4∫x^3 cosx dx

Now do all that again for each resulting integral, and the powers of x descends until you are left with just ∫sinx dx

Then just add all the pieces together.

Hmmm. I think you can save yourself some work. At x=0 all the terms with powers of x and sinx vanish.

at x=π/2 all the terms with cosx vanish (odd powers of x).

1. 👍 0
2. 👎 0
posted by Steve

Similar Questions

1. Multiplevariable calculus

Hello, I have to find the volume of the region enclosed by the paraboloid z=(x^2)+(y^2) and the planes z=1 and z=3 , so well i am struggling about the limits of each integral. I know that I can use cylindrical coordinates, but

asked by Alice on August 27, 2017
2. calculus

1. A sheet of cardboard 3 ft. by 4 ft. will be made into a box by cutting equal-sized squares from each corner and folding up the four edges. What will be the dimensions of the box with largest volume? so I did V=lhw and found

asked by Yoona on December 18, 2011
3. Calculus

I have a graph of f(x) which I cant post here, but would like some help with concepts. lim f(x) = L x->a I already found the limit for different values of a. Now I need to find the value of f(a) at each point. So is f(a) = lim

asked by George on July 7, 2015
4. Calculus

How do we evaluate the volume under the surface given by, z=2xsin(y) over the region bounded below by the curve y=x^2 and above by the line y=0 for 0

asked by Aryaa on October 26, 2019

Combine the following two integrals into one by sketching the region, then switching the order of integration. (sketch the region) im gonna use the S for integral sign..because idk what else to use.

asked by Sean on March 22, 2012
6. Statistics

Multiple Choice Which of the following statements is true about the 95% confidence interval of the average of a sample? A) 95 of 100 avgs of samples will be within the limits of the confidence interval. B) There is a 95% chance

asked by Andrew on July 26, 2013
7. Statistics

Can you please help with this question. The only thing that I have come up thus far is that I am using the z critical value because I am estimating a population proportion. Am I on the right track? An important issue facing

asked by Jim on March 25, 2008
8. double integrals

Combine the following two integrals into one by sketching the region, then switching the order of integration. (sketch the region) im gonna use the S for integral sign..lol SS6ycos(x^3-3x)dxdy+SS6ycos(x^3-3x) And the first

asked by Mary on March 21, 2012
9. linear programming

For the linear program Max 2A + 7B s.t. A + B greater than or equal to 12 2A + 2 B less than or equal too 26 B greater than or equal to 1 A, B greater than or equal to Which of the following would be found in the correct standard

asked by Donna on July 26, 2010