Difference between revisions of "Multivariate Calculus 10B, Problem 1"
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:: <span class="exam">a) <math>\int _0^1 \int_y^1 e^{\frac{y}{x}}~dxdy</math> | :: <span class="exam">a) <math>\int _0^1 \int_y^1 e^{\frac{y}{x}}~dxdy</math> | ||
:: <span class="exam">b) <math>\int_0^1 \int_0^{cos^{-1}(y)} e^{2x-y}~dxdy</math> | :: <span class="exam">b) <math>\int_0^1 \int_0^{cos^{-1}(y)} e^{2x-y}~dxdy</math> | ||
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'''solution(a):''' | '''solution(a):''' | ||
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|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> | |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> | ||
Revision as of 02:48, 7 February 2016
Calculate the following integrals
- a)
- b)
solution(a):
| Here we use change of variable, |
![{\displaystyle \int _{0}^{1}\int _{0}^{x}e^{\frac {y}{x}}~dydx=\int _{0}^{1}[xe^{\frac {y}{x}}|_{y=0}^{y=x}]~dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/21db579be5a60661ee94ecc30f930b30e12d7a53)