Top answers

What is the integral of sin(3x) cos(5x)?

Using trig formulas we have sin(5x+3x)= sin(5x)cos(3x)+cos(5x)sin(3x) and sin(5x-3x)= sin(5x)cos(3x) - cos(5x)sin(3x). Hence, sin(5x+3x) - sin(5x-3x) = sin(8x)-sin(2x) = 2cos(5x)sin(3x). This implies that co...
MN
Answered by Morenikeji N. • Maths tutor
6531 Views

solve 4^xe^(7x+5) = 21

ln((4^x)e^(7x+5)) = ln21; apply a natural log on both sides of the equation as an exponential containing e is involved ln4^x + ln(e^(7x+5)) = ln21; using logarithm rules you can seperate the single log on th...
WN
Answered by Wahib N. • Maths tutor
3859 Views

How do you integrate y = 4x^3 - 5/x^2?

First we should look at the formula for integrating x n . The integral is (x n+1 / n+1) + C. Let's break down our equation into two parts. The integral of 4x 3 = 4(x 3+1 / 3+1) = 4(x 4 / 4) = x 4 The integra...
HJ
Answered by Hannah J. • Maths tutor
5388 Views

Find the Total Area between the curve x^3 -3x^2 +2x and the x-axis, when 0 ≤ x ≤ 2.

Initally this question appears to be a straightforward integration that should be carried out between the limits of x=0 and x=2. However if this process is carried out, as strange result is obtained: Area = ...
WK
Answered by Will K. • Maths tutor
11855 Views

Why do we get cos(x) when we differentiate sin(x)?

If we have an equation for a line, it follows a certain shape when put it on Cartesian axes. If we wish to find the value of the gradient of the graph at a certain coordinate, we can use differentiation to g...
SH
Answered by Sophie H. • Maths tutor
7072 Views