Calculus Archive: Questions from December 24, 2022
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Calculate \( \iint_{S} f(x, y, z) d S \) For \[ y=2-z^{2}, \quad 0 \leq x, z \leq 7 ; \quad f(x, y, z)=z \] \( \iint_{S} f(x, y, z) d S= \)2 answers -
43 and 46 english please
43. \( S=\left\{(x, y) \mid x \geqslant 1,0 \leqslant y \leqslant 1 /\left(x^{3}+x\right)\right\} \) 44. \( S=\left\{(x, y) \mid x \geqslant 0,0 \leqslant y \leqslant x e^{-x}\right\} \) 45. \( S=\lef2 answers -
PLEASE SOLVE THIS WITH BETA GAMMA FUNCTION,,,,,,
3. Evaluate the following integrals: (WEEK 3) (i) \( \int_{0}^{\pi} \sin ^{5} \theta \cos ^{4} \theta d \theta \) (ii) \( \int_{0}^{\pi} \sin ^{6} \theta \cos ^{7} \theta d \theta \) (iii) \( \int_{0}2 answers -
Solve the initial-value problem (IVP) \[ y^{\prime}=\sec \left(\frac{y}{x}\right)+\frac{y}{x} \quad, \quad y(1)=\frac{\pi}{2} \]2 answers -
2. Evaluate in terms of beta function: (WEEK 3) (i) \( \int_{0}^{1} \frac{x^{2}}{\sqrt{1-x}} d x \) (ii) \( \int_{0}^{1} x^{7}(1-x)^{3} d x \) (iii) \( \int_{0}^{1} \frac{1}{\sqrt{1-x^{3}}} d x \) (iv2 answers