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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...

Answered by Morenikeji N. • Maths tutor

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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 singl...

Answered by Wahib N. • Maths tutor

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

First we should look at the formula for integrating xⁿ. The integral is (xⁿ⁺¹/ n+1) + C.

Let's break down our equation into two parts.

The integral of 4x
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Answered by Hannah J. • Maths tutor
4556 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...

Answered by Will K. • Maths tutor

10312 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 t...

Answered by Sophie H. • Maths tutor

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