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Integrate x^2e^x with respect to x between the limits of x=5 and x=0.

This question is to test integration by parts. First let u=x 2 and u'=2x as a result, and v'=e x and so v=e x too. Then use the by parts formula to express the integral as x 2 e x ​​​​​​​-2(integral of):(xe ...
AA
Answered by Alex A. • Maths tutor
6496 Views

What is the turning point on the curve f(x) = 2x^2 - 2x + 4

df/dx = 4x - 2 turning point when differential = 0 ==> 4x = 2 hence; x = 0.5 When x = 0.5 f(x) is equal to (substitute) 3.5 hence the turning point is at (0.5,3.5)
DT
Answered by David T. • Maths tutor
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How do I find the solution of the simultaneous equations x+3y=7 and 5x+2y=8

By looking at both equations you spot that the 'x' in the first equation has coefficient equal to 1, so it would be quite convenient to make 'x' the subject of the first equation and then substitute what 'x'...
NB
Answered by Nicola B. • Maths tutor
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Write down three linear factors of f(x) such that the curve of f(x) crosses the x axis at x=0.5,3,4. Hence find the equation of the curve in the form y = 2(x^3) + a(x^2) + bx + c.

the curve crosses the graph at the x axis at 0.5,3 and -4 so f(0.5)=0, f(3)=0,f(-4)=0. All linear factors are the form of g(x)=(x-a) so 0=g(0.5)=0.5-a. rearranging we get that a=0.5 ie g(x)=x-0.5 similarly t...
KT
Answered by Kishan T. • Maths tutor
7126 Views

Integral of 1/(x^3 + 2x^2 -x - 2)

Factorise denominator using the factor theorem giving - 1/(x+1)(x+2)(x-1) Use partial fractions to turn this into an easier form to integrate giving - 1/3(x+2) + 1/6(x-1) - 1/2(x+1) using integral 1/x = ln(x...
MO
Answered by Mojowo O. • Maths tutor
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