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Using the substitution x = 2cosu, find the integral of dx/((x^2)(4-x^2)^1/2), evaluated between x=1 and x=sqrt(2).

Starting with x=2cosu, rearrange for u to get u=arccos(x/2), then find the upper and lower limits of the integral. We find that our lower limit goes from 1 to pi/3, ad our upper limit goes from root 2 to ...

TD
Answered by Tayn D. Maths tutor
7386 Views

Calculate the integral of e^x*sin x

1/2 *e^(x)(sin x -cos x)

Answered by Maths tutor
2908 Views

integrate arcsin(x)

Use integration by parts to obtain:u=arcsin(x), u'=1/(1-x2)0.5, and v'=1, v=x
Using the equation: integral of uv' = uv - integral of u'vintegral of arcsin(x) = xarcsin(x) - inte...

MG
Answered by Maya G. Maths tutor
1403 Views

The perimeter of a right-angled triangle is 72 cm. The lengths of its sides are in the ratio 3 : 4 : 5 Work out the area of the triangle.

72 / (3+4+5) = 6base :36 = 18height :46 = 24area = (base * height) /2area = (18*24)/2=216 cm ^2

IH
Answered by Ibrahim H. Maths tutor
2491 Views

Solve x^2+6x+1=0 by completing the square

x2+6x+5=0 First of all half the x coefficient and write (x+6/2)2 the take away the (6/2)2 and add on the 5
(x+3)2-9+5=0
(x+3)2-4=0 ...

BS
Answered by Ben S. Maths tutor
7625 Views

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