Math  /  Calculus

Question(b) (5 points) 02010yexdxdydz\int_{0}^{2} \int_{0}^{1} \int_{0}^{y} e^{x} d x d y d z

Studdy Solution
Finally, integrate the result with respect to zz. The limits for zz are from 00 to 22:
02(e2)dz\int_{0}^{2} (e - 2) \, dz
Since e2e - 2 is a constant, the integral is straightforward:
(e2)021dz=(e2)[z]02=(e2)(20)=2(e2)(e - 2) \int_{0}^{2} 1 \, dz = (e - 2) \cdot [z]_{0}^{2} = (e - 2) \cdot (2 - 0) = 2(e - 2)
The value of the triple integral is:
2(e2)\boxed{2(e - 2)}

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord