# Calculus AP

Evaluate the integral
interval from [0 to pi] t sin(3t)dt
Use integration by parts
u=t and dv=sin(3t)dt. then du=dt and v=-cos(3t)/3

here is my problem but Im having problem to solve with pi.

∫t sin(3t)dt
= -tcos(3t)/3 - ∫[-cos(3t)/3]dt
=-tcos(3t)/3 + sin(3t)/9 ](o,pi)

1. 👍 0
2. 👎 0
3. 👁 680
1. Your integral is correct, so we get

[ -πcos(3π) /3 + sin(3π) /9] - [ 0 + sin(0)/9]
= -π(-1)/3 + 0/9 - 0
= π/3

1. 👍 0
2. 👎 0

1. 👍 0
2. 👎 0

## Similar Questions

1. ### calc

evaluate the integral: y lny dy i know it's integration by parts but i get confused once you have to do it the second time Leibnitz rule (a.k.a. product rule): d(fg) = f dg + g df y lny dy = d[y^2/2 ln(y)] - y/2 dy ----> Integral

2. ### calculus

1.Evaluate the integral. (Use C for the constant of integration.) integral ln(sqrtx)dx 2. Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the curves about the given axis. y =

3. ### Calculus

Integral of sin2xcos3x using Integration by Parts

4. ### calculus2

Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of integration.) ∫√((x^2-4)/x)dx x=2sec(t)

1. ### calc: avg value

Find the average value of the function "f(x) = x^2 sqrt(1+x^3)" on the interval [0,2]. and this is what i did.. please check for mistakes. thanks :D f(x) = x^2 sqrt(1+x^3), [0,2] f ave = (1/(b-a))*inegral of a to b for: f(x) dx f

2. ### calculus integrals

Evaluate the integral by making the given substitution. (Use C for the constant of integration. Remember to use absolute values where appropriate.) integral x^5/x^6-5 dx, u = x6 − 5 I got the answer 1/6ln(x^6-5)+C but it was

Evaluate the integral by using substitution. Use an upper-case "C" for the constant of integration. integral x^5((x^6-2)^10)dx ty

4. ### calculus

Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) (x^2−x+12)/(x^3+3x) dx

1. ### Calc

Evaluate the integral by reversing the order of integration.(2 integrals) 0 to 4 5ex2 dx dy 3y to 12

2. ### Calc

Evaluate the integral by reversing the order of integration. (2 integrations) 0 to 1 sqrt(x) to 1 8(y^3+1) dy dx

3. ### Calculus

A steady wind blows a kite due west. The kite's height above ground from horizontal position x = 0 to x = 80 ft is given by the following. y = 150 - (1/40)(x-50)^2 Find the distance traveled by the kite. y = 150 - (1/40)(x-50)^2 y

4. ### math

I'm trying to find the convolution f*g where f(t)=g(t)=sin(t). I set up the integral and proceed to do integration by parts twice, but it keeps working out to 0=0 or sin(t)=sin(t). How am I supposed to approach it? integral