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How do I integrate 4x*exp(x^2 - 1) with respect to x?

During the session I would go step by step through the integration by substitution.

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Integrate (1 - x^2)^(-0.5)dx within the limits 0 and 1

The answer is π/2. The key trick to solving this problem is to change variables by using the substitution x = sin(θ). We then need to change the differential and the limits too.

Answered by Cameron W. • Maths tutor

3434 Views

Differentiate y = x^3− 5x^2 + 3x

the rule for differentiating in terms of x is to multiply by the power then decrease the power by one. So going through the equation x^3 will be multiplied by 3 and go to x^2 so will be 3x^2. Then its imp...

Answered by Georgia D. • Maths tutor

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Supposing y = arcsin(x), find dy/dx

Suppose:
y = arcsin(x)
Then, x = sin(y)
And, dx/dy = cos(y) ----- (1)
Using: dy/dx = 1/(dx/dy);
Thus 1 becomes: dy/dx = 1/cos(y) ------ (2)
Using: sin^2(y) + cos^2(y) = 1;

Answered by James N. • Maths tutor

6518 Views

Find the coordinates of the turning points of the curve y = 4/3 x^3 + 3x^2-4x+1

First differentiating by the rule that xⁿ differentiates to nx^n-1 we have that dy/dx = 4x²+6x-4.
At the turning points of a curve the differential is equal to 0 so w...

Answered by Theo E. • Maths tutor

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