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Find the solutions of the equation 3cos(2 theta) - 5cos(theta) + 2 = 0 in the interval 0 < theta < 2pi.

3cos^2(theta) - 3sin^2(theta) - 5cos(theta) + 2 = 0 3cos^2(theta) + 3cos^2(theta) - 3 - 5cos(theta) + 2 = 0 6cos^2(theta) - 5cos(theta) - 1 = 0 delta = 25 + 24 = 49 cos(theta) = (5 - 7)/12 = -1/6 or cos(thet...
PW
Answered by Piotr W. • Maths tutor
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I'm trying to integrate f(x)=sin(x) between 0 and 2 pi to find the area between the graph and the axis but I keep getting 0, why?

(First draw graph of sin(x) and mark 0 and pi and 2 pi) In short, you will need to split up your integral into two parts. One from 0 to pi and one from pi to 2 pi? Can you see/guess why this might be? First ...
JB
Answered by Jack B. • Maths tutor
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How do I find a stationary point? And how do I determine whether it is a maximum or minimum point?

In order to find the stationary points of any funcion, you must differentiate. Once you have differentiated, the deriviate of this function must be set equal to 0, in order to determine what the stationary p...
NA
Answered by Neelam A. • Maths tutor
19935 Views

Find the gradient of the curve y=sin(x^2) + e^(x) at the point x= sqrt(pi)

y=sin(x 2 ) + e x Firstly we need to differentiate. dy/dx = 2xcos(x 2 ) + e x using the chain rule Notice the gradient at x = sqrt(pi) is found when we sub x into dy/dx Hence dy/dx = 2*sqrt(pi) cos( sqrt(pi)...
JR
Answered by Jordan R. • Maths tutor
7464 Views

Find the indefinite integral of Ln(x)

This question requires integration by parts, using the formula: Integral(u dv) = u v - integral(v du) This is applied to find the integral of Ln(x) by writing Ln(x) as 1 * Ln(x), u is then Ln(x) and dv is 1....
TD
Answered by Tutor66529 D. • Maths tutor
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