# Area under the curve!

• September 24th 2009, 10:37 AM
Oasis1993
Area under the curve!
Hello everyone.
I would really appreciate it if you helped me out with this question.

Find the are of the region shaded in the diagram.

The equation of the curve is y=3x^8+5

I found the x points as -1 and 1 but i cant seem to get further.

Thank you.
• September 24th 2009, 10:41 AM
tutor.mathitutor
y1=3x^8+5
y2 = 8

Area of the shaded region = Integration(y2-y1)dx over -1 to 1 will give you the area. This integration is very straight forward.
• September 24th 2009, 10:58 AM
Oasis1993
could you please make it more clear.
y2=8?
• September 24th 2009, 11:04 AM
tutor.mathitutor
y2 = 8 is the straight line in your diagram below which the shaded region is shown.
• September 24th 2009, 01:52 PM
skeeter
Quote:

Originally Posted by Oasis1993
Hello everyone.
I would really appreciate it if you helped me out with this question.

Find the are of the region shaded in the diagram.

The equation of the curve is y=3x^8+5

I found the x points as -1 and 1 but i cant seem to get further.

Thank you.

the method is the same as the other problem you posted ...

$\int_{-1}^1 8 - (3x^8+5) \, dx$

or, using symmetry, ...

$2 \int_0^1 8 - (3x^8+5) \, dx$