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Integrate x/((1-x^2)^0.5) with respect to x

x = sin(u), dx/du = cos(u), dx = cos(u) * du,[x/(1-x^2)^0.5)] * dx = [sin(u)/((1-(sin(u)^2))^0.5] * cos(u) * du = [sin(u)/(cos(u)^2)^0.5] * cos(u) * du = sin(u) * duIntegral of sin(u) * du = -cos(u) = -(1-si...
AP
Answered by Andrew P. • Maths tutor
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‘People will do anything, no matter how foolish, to get what they want’ - In the light of this view, discuss ways in which Webster represents ambition in The Duchess of Malfi.

The character Bosola is a man who has suffered unfairly at the hands of those he has worked for, leading him to become a man who can no longer trust those around him and leaving him with very little compassi...
AC
Answered by Arthur C. • Music tutor
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Express 5/[(x-1)(3x+2)] as partial fractions.

5 = a(3x+2) + b(x-1), x = 1, 5 = a(3+2) +b (1-1), 5 = a(5) + b(0), 5 = 5a, a = 1, x = -2/3, 5 = a(-2+2) + b(-(2/3)-1), 5 = a(0) + b(-5/3), 5 = -5b/3, b = -3, Therefore: 5/[(x-1)(3x+2)] = 1/(x-1) -3/(3x+2)
AP
Answered by Andrew P. • Maths tutor
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Compare and contrast the portrayal of the relationship Mrs Linde and Nora have with their parents.

Nora treatment of her father - leaving him on his deathbed - contrasts highlight with Mrs Linde's treatment, as she chose to care for her sick parent. Nora's treatment is reflective of her childlike nature, ...
MP
6850 Views

Differentiate sin(x)cos(x) with respect to x?

You will have to use the Product Rule. The Product rule: when y=f(x)g(x), then dy/dx=f'(x)g(x)+f(x)g'(x). In this example, f(x)=sin(x) and g(x)=cos(x). Hence f'(x)=cos(x) and g'(x)=-sin(x). Using these and s...
MM
Answered by Matthew M. • Maths tutor
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