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Find the definite integral of f(x) = 12/(x^2+10x+21) with limits [-1,1]. Give your answer to 2 decimal places.

Factorising denominator of fraction: x^2 + 10x + 21 = (x+3)(x+7) 2) Partial fractions: f(x) = 12/(x+3)(x+7) ; let f(x) = A/(x+3) + B/(x+7) then equating the nominator: A(x+7) + B(x+3) = 12 From this we can s...
CG
2820 Views

Why does tanx = sinx/cosx ?

This identity can easily be shown by asking the student to draw a right-angled triangle, with one of the remaing two angles labelled x, and labelling the respective oppposite, adjacent and hypotenuse sides O...
SR
16002 Views

A straight line passes trough the points A(-4;7); B(6;-5); C(8;t). Use an algebraic method to work out the value of t.

We can write the equation of a straight line like y=ax+b, where a and b are constants. If a point is on the line, the equation will be true for the x,y of the point.Now start with point A: 7 = (-4)a + b. Res...
MF
7896 Views

(x+4)((x^2) - kx - 5) is expanded and simplified. The coefficient of the x^2 term twice the coefficient of the x term. Work out the value of k.

(x + 4) (x 2 - kx - 5) = x 3 - kx 2 - 5x + 4x 2 - 4kx - 20 = x 3 + (4-k)x 2 + (-5-4k)x - 20.The coefficients are: (4-k) of x 2 and (-5-4k) of x. Now we can write the equation:(4-k) = 2(-5 - 4k) /expand4 - k ...
MF
10520 Views

Find the coordinates of the stationary points on the curve y=x^5 -15x^3

dy/dx = 5x 4 -45x 2 by multiplying each term by the power and then decreasing the power by oneAt stationary points, dy/dx=0 since the function is neither increasing nor decreasing at a stationary point5x 4 -...
SD
5843 Views