Multivariate Calculus 10B, Problem 1

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

Step 1:
Here we use change of variable, Failed to parse (syntax error): {\displaystyle \int _0^1 \int_0^x e^{\frac{y}{x}}~dydx = \int _0^1[\frac{1}{x}e^{\frac{y}{x}}\right|_{y = 0}^{y = x}}