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How to prove that Integral S 1/(a^2+x^2) dx= 1/a arctan(x/a) + C ?

In order to answer this question, at first we need to use the method of substitution. That means, we're trying to replace x with a different variable u. Lets use the substitution of x = a tan u, then du/d...

JW
Answered by Judyta W. Maths tutor
5285 Views

Solve the following simultaneous equations: x^2 + 2y = 9, and y = x + 3.

Label the two equations as the following: x2 + 2y = 9 y = x + 3 Equation 2 can be substituted into equation 1, giving: x2 + 2( x + 3 ) = 9Expanding the brackets and subtracting ...

XB
Answered by Ximena B. Maths tutor
4078 Views

How do I solve simultaneous equations by substitution?

You can solve simultaneous equations by either substitution or elimination. Say we have the equations:(1) 8y + 6x = 24 and (2) 2y - x = 6SUBSTITUTION METHODFirst, you need to find x in terms of y (or y in...

JN
Answered by Joshua N. Maths tutor
2838 Views

Find all values of x in the interval 0 ≤ x ≤ 2pi for 2sin(x)tan(x)=3

This questions involves the use of trigonometric identities, specifically [1] tan(x) = sin(x)/cos(x) and [2] sin2(x) + cos2(x) = 1.
Start by rearranging the given equations to ...

JC
Answered by Jasmin C. Maths tutor
6500 Views

Find the derivative of sin(x)/x^3 with respect to x

First, bring the x to the numerator (top) as x^(-3). Then use the chain rule: State the first times derivative of the second plus state the second times the derivative of the first.State sin(x), then mult...

TD
Answered by Tutor170145 D. Maths tutor
6336 Views

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