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find the integral of y=x^2 +sin^2(x) with respect to x between the limits 0 and pi

intergal 0 pi (x^2 + sin^2(x))dx = integral 0 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)thereforeintegral 0 pi (x^2 +sin^2(x))dx = [(x^3)/3...
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Integrate xsin(x) with respect to x

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, us...
EM
Answered by Ethan M. • Maths tutor
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A ball is kicked and has an instantaneous velocity of 19.6m/s at an angle of 30 degrees to the horizontal. A target lies flat on the ground in the direction the ball is kicked and lies at a distance of (98/5)*(3^1/2)m. Does the ball land on the target?

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 and t...
AS
Answered by Alexander S. • Maths tutor
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A car is accelerating at 2 ms^-2 along a horizontal road. It passes a point A with a velocity of 10 ms^-1 and later a point B, where AB = 50m. FInd the velocity of the car as it passes through B.

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, of ...
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find the gradient of y=x3 X0=5

dx/dy = 3(x)2substitute x = 5so (5) squared 253 times 25 = 75
JA
Answered by Jenna A. • Maths tutor
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