Difference between revisions of "Multivariate Calculus 10B, Problem 1"

Revision as of 02:46, 7 February 2016

Calculate the following integrals

a)

\int _{0}^{1}\int _{y}^{1}e^{\frac {y}{x}}~dxdy

b)

\int _{0}^{1}\int _{0}^{cos^{-1}(y)}e^{2x-y}~dxdy

'solution(a):


Here we use change of variable, $\int _{0}^{1}\int _{0}^{x}e^{\frac {y}{x}}~dydx=\int _{0}^{1}[xe^{\frac {y}{x}}\|_{y=0}^{y=x}]~dx$

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 :: <span class="exam">b) <math>\int_0^1 \int_0^{cos^{-1}(y)} e^{2x-y}~dxdy</math>
-'''solution:'''
+'''solution(a):''
-'''a'''
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-!Step 1: &nbsp;
+!
 |-
 |Here we use change of variable, <math>\int _0^1 \int_0^x e^{\frac{y}{x}}~dydx = \int _0^1[xe^{\frac{y}{x}}|_{y = 0}^{y = x}]~dx</math>