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Factorise f(x)=3x^3+8x^2-20x-16 completely

First we need to use the factor theorem to find a factor.f(1)=-25 so x-1 is not a factorf(-1)=9 so x+1 is not a factorf(2)=0 so x-2 is a factorSo x-2 is our starting point, we need to polynomial division f(x...
LB
Answered by Luke B. • Maths tutor
5881 Views

Use the substitution u=cos(2x)to find ∫(cos(2x))^2 (sin(2x))^3dx

Step 1 differentiate substitution: du/dx = -2sin(2x)Step 2 rearrange for dx: dx=du/-2sin(2x)Step 3 substitute: integral= ∫u 2 sin 3 (2x).du/-2sin(2x)Step 4 get the integral in terms of u by cancelling: integ...
NA
Answered by Nabeel A. • Maths tutor
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Calculate dy/dx for y=x(x−1)

y=x(x−1)y= x^2-xdy/dx= 2x-1
BS
Answered by Bella S. • Maths tutor
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Integrate using by parts twice : ∫e^(x)*(cos(x))dx

By putting u=cosx and v’= e^x , use the by parts formula to get:∫e^(x) (cos(x)) dx = cos(x)e^x - ∫-(e^x)sin(x) dx. Use by parts again on the second term to get ∫ =cos(x)e^x + sin(x)e^x - ∫e^(x) (cos(x))dx. T...
IZ
Answered by Isma Z. • Maths tutor
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Integrate ((7e^(x/2))/4) with respect to x within the bounds of x=0 and x=2. (Basic introduction to definite integration)

Check to see if anything can be removed from withing the integral and taken out the front. In this case, 7/4 can be taken out the front (as it is not dependent on x), leaving only the term e^(x/2) to be inte...
NM
Answered by Niall M. • Maths tutor
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