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How would the integral ∫x^2sin2xdx be solved using integration by parts?

The general formula for integration by parts is given as
∫u(dv/dx)dx = uv - ∫v(du/dx)dx
given that the equation to be solved is ∫x²sin2xdx, the values for u, v, du/dx and dv/dx can ...

Answered by Samuel N. • Maths tutor

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A stone is thrown from a bridge 10m above water at 30ms^-1 30 degrees above the horizontal. How long does the stone take to strike the water? What is its horizontal displacement at this time?

The first thing to do for part a) is work out the vertical component of the velocity. By drawing a triangle where 30m/s is the hypotenuse with angles of 30 degrees, 90 degrees, and 60 degrees, and by appl...

Answered by Sarah U. • Maths tutor

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What is the derivative of f(x)=sqrt(3x+2)=(3x+2)^(1/2)?

By the power rule, the derivative of x^(n) is nx(n^1) and by the chain rule, the derivative of g(h(x)) is g'(h(x))h'(x).
Let g(x)=x^(1/2) and h(x)=3x+2 so that f(x)=g(h(x)).

Then by the power...

Answered by Luke P. • Maths tutor

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A circle C with centre at the point (2, –1) passes through the point A at (4, –5). Find an equation for the circle C.

You would start with this equation (x – a)² + (y – b)² = r², with the center being at the point (a, b) and the radius being "r". Therefore you would have (x-2)

Answered by Ishan N. • Maths tutor

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Find the indefinite integral of cos^2 x

First, we need to write cos²x in a form that is easily integrable. We can use the double angle formula cos(2x) = 2cos²x - 1 to see that cos²x = 1/2cos(2x)+1/2. Now, we can...

Answered by Ethan R. • Maths tutor

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