integral and average value?!

[pakakid]

Hey guys I have a upcoming test and my teacher gave us 4 practice problems. Can anyone help me with any of them? They deal with integrals and finding area of region. I scanned the 4 questions in the link below.

http://yfrog.com/eoimg003njj

Thank you in advance

 

[galactus]

#1: \(\displaystyle \int_{\frac{\pi}{6}}^{\frac{\pi}{3}}csc(x)cot(x)dx\)

Let \(\displaystyle u=cot(x), \;\ -du=csc(x)dx\)

 

[Deleted member 4993]

Hey guys I have a upcoming test and my teacher gave us 4 practice problems. Can anyone help me with any of them? They deal with integrals and finding area of region. I scanned the 4 questions in the link below.

http://yfrog.com/eoimg003njj

Thank you in advance

These problems have no trickery involved. Where are you stuck exactly?

1_d

\(\displaystyle \int \frac{3x^2+6x}{\sqrt{3x^2+x^3}}dx\)

substitute

\(\displaystyle u \ = \ \sqrt{3x^2+x^3}\)

and continue.....

 

[pakakid]

1)cscx cotx dx = -csc x +C
2)5x^2/2 - 1/5 cos(5x) +c
3)-1/2cos(pix^2)
4)2 radical (3x^2+x^3)

Thank you!

For 2a is the correct formula= integral of x^2-3 + x^2+1. Solving from 10 to 5?

For b, i think the equation would be the same i just dont understand the boundaries. what does it mean hen bounded by h(x) ans g(x)?

 

[Deleted member 4993]

1)cscx cotx dx = -csc x +C
2)5x^2/2 - 1/5 cos(5x) +c
3)-1/2cos(pix^2)
4)2 radical (3x^2+x^3) + C

Thank you!

For 2a is the correct formula= integral of x^2-3 + x^2+1. Solving from 10 to 5?

For b, i think the equation would be the same i just dont understand the boundaries. what does it mean hen bounded by h(x) ans g(x)?