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Solve the following integral: ∫ arcsin(x)/sqrt(1-x^2) dx

We will solve the integral by part. We know the formula for integration by parts: ∫ f(x)'g(x)dx=f(x)g(x)-∫f(x)g(x)'dx (1) . We know that: (arcsin (x))'=1/sqrt(1-x^2) . So we can write arcsin(x)/sqrt(1-x^2) d...
IC
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How do I use product rule when differentiating?

Problems like this usually look something like: Find the differential of (x 2 e 2x ). The product rule is used when we have to differentiate two different functions multiplied by eachother, so we should alwa...
JK
Answered by Jasvir K. • Maths tutor
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In the case of vectors, how do I find the shortest distance between a point and a line?

The key word in the question is 'shortest'. The shortest distance from a point to a line is always the perpendicular distance. If we calculate the appropriate angles and lengths/distances, we can use trigono...
SK
Answered by Saskia K. • Maths tutor
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Binomial expansion of (1+4x)^5 up to x^2

This question can be treated like a normal binomial expansion question which is commonly seen at A level. The standard binomial expansion is (1+x) n = 1 + nx + (n(n-1)(x 2 ))/2! where 2! is 2 factorialSo in ...
KI
Answered by Katherine I. • Maths tutor
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Find the gradient of the equation y=e^2x.ln(4x^2) when x=5.

>First know that you must differentiate to find the gradient. To differentiate this function you must use the product rule which is:>d/dx(f(x)g(x))=f(x)g'(x)+f'(x)g(x)>Now apply this rule to the for...
AS
Answered by Akshina S. • Maths tutor
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