# area between curve and x-axis

• Jun 2nd 2010, 06:44 AM
Punch
area between curve and x-axis
Find the area bounded by the following:

$\displaystyle y=\frac{1}{\sqrt{3x+7}} ; x=-1, x=3,x-axis$
• Jun 2nd 2010, 07:20 AM
TheEmptySet
Quote:

Originally Posted by Punch
Find the area bounded by the following:

$\displaystyle y=\frac{1}{\sqrt{3x+7}} ; x=-1, x=3,x-axis$

$\displaystyle \int_{-1}^{3}\frac{dx}{\sqrt{3x+7}}\,\, ;u=3x+7 \implies du=3dx \implies \frac{1}{4}\int_{4}^{16}u^{-\frac{1}{2}}du$
• Jun 2nd 2010, 09:54 AM
pythagorian
Correct me if I am wrong
Quote:

Originally Posted by Punch
Find the area bounded by the following:

$\displaystyle y=\frac{1}{\sqrt{3x+7}} ; x=-1, x=3,x-axis$

Correct me if I am wrong, but I believe the multiplier outside of the integral should be one third
• Jun 3rd 2010, 06:04 PM
Punch
sorry emptyset.. but i dont understand the part where u wrote $\displaystyle \int_{4}^{16}u^{-\frac{1}{2}}du$

isnt it suppose to be 3 on top and -1 below?
• Jun 3rd 2010, 07:11 PM
Diemo
Those are the limits for x, but you are now working with the variable u = 3x+7.

Check out what the values of u are when x=-1 and x=3.