Use the transformation u = 3x + 4y, v=x+4y to evaluate the given integral for the region R bounded by the lines y = - SS (3x²+ R 3 1 -2x+1, y=-x+2, y=-x, and y=-x+2. + 16xy + 16y²) dx dy

Q: Solve the given initial value problem. y" + 2y' = 0; y(0) - 7, y'(0) = -4 = The solution is y(t) =…

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Q: Evaluate the integral ſſ /ydA, where T- triangle with vertices (1,0), (0, 1), (1, 1).

A: Let us consider the double integral  I=∫ab∫f(x)g(x) f(x,y) dydx    or I=∫ab∫f(y)g(y) f(x,y) dxdy…

Q: Evaluate the integral -7 dx Væ +1+ Vx + C

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Q: 5) Consider the parallelogram with vertices (0,0), (4,0), (6,2) & (2, 2). We know the area of this…

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Q: Use a substitution of u = r to integrate : dr.

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Q: Compute the integral 4x + 8x³ dx. x4 + 16

A: The given integral is, ∫4x+8x3x4+16dx. Rewrite the given integral as follows.…

Q: Find area of region x = 45 − 5y2,  x = 5y2 − 45

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Q: Evaluate the integral dx (2x + 4)* by making the appropriate substitution: u = dx (2x + 4)°

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