Integration question

Here's the question:

Sketch on the same diagram the curve y = x^3 and the lines y = 1 and y = 8. Find the area enclosed by the curve y = x^3, the lines y = 1 and y = 8 and the y axis

I found the area between the y axis and the curve from y = 0 and 8 but it's apparently not correct, I also tried adding that to the area between the x axis and the curve from x = 0 to 2 because (2,8), please help, apparently the answer is 45/4 🙂

Reply 1

3pointonefour

18

Original post by Freedom physics

Here's the question:

Sketch on the same diagram the curve y = x^3 and the lines y = 1 and y = 8. Find the area enclosed by the curve y = x^3, the lines y = 1 and y = 8 and the y axis

I found the area between the y axis and the curve from y = 0 and 8 but it's apparently not correct, I also tried adding that to the area between the x axis and the curve from x = 0 to 2 because (2,8), please help, apparently the answer is 45/4 🙂

Since you're finding area along the y-axis, you want to integrate a function of y. So write y=x^3 in the form x=... Then use 8 and 1 as your limits, remembering to integrate in respect to y.

Reply 2

Freedom physics

OP

12

I've done ( .25 x (8)^4 ) - ( .25 x (1)^4 ), what am I doing wrong? 😄🙂

Reply 3

3pointonefour

18

Original post by Freedom physics

I've done ( .25 x (8)^4 ) - ( .25 x (1)^4 ), what am I doing wrong? 😄🙂

You're integrating with respect to x still. You only integrate with x if you're finding area along the x-axis. But since you want region bounded by y-axis, write x=y^(1/3) then integrate with limits as 8 and 1.