Wednesday

August 27, 2014

August 27, 2014

Posted by **m** on Wednesday, February 23, 2011 at 3:00pm.

interval [0; 2]. Compute mA.

what is lim mA as A goes to infinite?

- calculus -
**MathMate**, Wednesday, February 23, 2011 at 7:21pmmA is the integral divided by the length of the interval, namely 2-0=2.

I=∫sin(Ax)^3dx

Substitute

u=cos(Ax),

du =-Asin(Ax)dx

so

I=-(1/A)∫(1-u²)du

=-(1/A)[u-u³/3] from 0 to 2

=(cos^3(2A)-cos^3(0)-3cos(2A)+3cos(0))/3A

=(cos^3(2A)-3cos(2A)+2)/3A

mA = I/2 = (cos^3(2A)-3cos(2A)+2)/6A

For the second part, take the limit as A->∞.

**Related Questions**

Calculus - I'm supposed to find the average value of the function over the given...

calculus - Suppose f'(x) = xe^-x^2. a) On what interval is f increasing? On what...

CALCULUS - What is the following limit? lim as n goes to infinity of (pi/n) (sin...

CALCULUS LIMITS - What is the following limit? lim as n goes to infinity of (pi/...

Calculus - What is the following limit? lim as n goes to infinity of (pi/n) (sin...

Calculus - Does the series (1+sin(n))/(10^n) from summation 0 to positive ...

Calculus - Find the positive integers k for which lim ->0 sin(sin(x))/x^k ...

Calculus - Find the limit. lim 5-x/(x^2-25) x-->5 Here is the work I have so ...

calculus-limits?? - i keep on doing something wrong on this problem,i guess im ...

calculus - Consider the given function and the given interval. f(x) = 4 sin x &#...