Top answers

Integral between 0 and pi/2 of cos(x)sin^2(x)

The key point in here is noticing that the derivative of sin(x) is cos(x). That way, if we rename sin(x) as u , i.e u:=sin(x), the derivative will be du=cos(x)dx. So, inside the integral, instead of having c...
ML
Answered by Maria L. • Maths tutor
6493 Views

What is the derivative with respect to x of the function f(x)=1+x^3+ln(x), x>0 ?

Despite the hideous view, we can apply to this function the same methodology as all the other ones: break it down to pieces. What we mean is that we recognize three terms inside f(x): one is the number 1 alo...
ML
Answered by Maria L. • Maths tutor
3882 Views

Where does integration by parts come from?

The best way to do well in maths, is to learn where things come from. Mastering the basics makes everything else much easier! To start, consider the product rule with two functions u(x) and v(x) (using dashe...
TM
Answered by Tom M. • Maths tutor
3652 Views

Integrate (12x^5 - 8x^3 + 3)dx giving the terms of the answer in the simplest terms

Integration is essentially differentiation in reverse! So in the simpler cases instead of multiplying by the power of x and subtracting one from the power of x, you add one to the power of x and divide by th...
ES
Answered by Ellen S. • Maths tutor
7018 Views

(C3) Show that 4csc^2(x) - cot^2(x) = k can be expressed as sec^2(x) = (k-1)/(k-4) where k != 4

The student can answer this in several ways. One using the simple, known identities csc= 1/sin, cot=1/tan, sec=1/cos, tan=sin/cos, sin^2 + cos^2 = 1 and basic algebra is the following: 4csc^2 - cot^2 = k4/si...
FH
Answered by Fearghus H. • Maths tutor
4367 Views