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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
4946 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

11123 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

5766 Views

Prove that the lines 2y=3-x and y-2x=7 are pependicular.

We can find out whether lines are perpendicular by comparing their gradients. Each gradient should be the negative reciprocal of the other - for example, 3/2 and -2/3, or 4 and -1/4. (Writing the number a...

Answered by Pranavi M. • Maths tutor

3577 Views

Integrate 3 sin(x) + cos(2x)

Here is an example of integration where you would use the chain rule. You would begin by integrating 3sin(x) to get -3cos(x) and then cos(2x) to get 1/2sin(2x). This is because whatever is multiplied by t...

Answered by Dannielle S. • Maths tutor

8152 Views