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intergal₀^pi(x^2 + sin^2(x))dx = integral₀^pi(x^2 + 1/2 - cos(2x)/2)dx since sin^2(x) + cos^2(x) = 1cos^2(x) - sin^2(x) = cos(2x)2sin^2(x) = 1 - cos(2x)thereforei...

For this use integration by parts, letting the integral = T. Let u = x and dv/dx = sin(x). Differentiating u with respect to x gives du/dx = 1. Integrating dv/dx with respect to x gives v = - cos(x). Now,...

First assume air resistance is negligible.Draw a diagram for the problem, this makes picturing it a lot easier.Next calculate the horizontal and vertical velocity of the ball. With the aid of a diagram an...

From the first look, we can see the question states the car is undergoing constant acceleration, thus we know the SUVAT equations are valid. Then reading on, we're required to find the final velocity, v, ...

dx/dy = 3(x)2substitute x = 5so (5) squared 253 times 25 = 75