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How do you do integration by parts?

When you see a complicated product, split it into the form u.v', where u and v' are algebraic expressions such as x^2. You can then use the formula: uv'=uv-integral(vu') which you would take between any limi...
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Answered by Andrew B. • Maths tutor
3458 Views

Find the equation of the normal line at the point H, where θ= π/6, on the curve with equations x=3sinθ and y=5cosθ

Step 1: We begin solving this problem by finding the gradient of the tangent line at H, which is equal to dy/dx. In this case, our curve has equations x = 3sinθ and y= 5cosθ. Now, we differentiate x and y wi...
PK
Answered by Pantelis K. • Maths tutor
9182 Views

Express (3x^2 - 3x - 2)/(x-1)(x-2) in partial fractions

Step 1: When asked to exrpess something in partial fractions, we first compare the power of the numerator to the power of the denominator. In our case we have that the power of quadratic equation in the nume...
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Answered by Pantelis K. • Maths tutor
19521 Views

A curve has equation y = 6ln(x) + x^2 -8x + 3. Find the exact values of the stationary points.

When thinking about stationary points, it is important to remember that these points happen when the gradient of the curve is 0 (-> dy/dx = 0), or if you prefer, when the rate of change of a graph is 0. S...
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Answered by Christopher P. • Maths tutor
7058 Views

Find dy/dx when y = x^2(cos(x)).

y = x 2 (cos(x)) therefore we will need to use the product rule, dy/dx = u dv/dx + v du/dx where u = x 2 and v = cos(x) du/dx = 2x and dv/dx = - sin(x), (don't forget the negative symbol when differentiating...
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Answered by Joseff S. • Maths tutor
32847 Views