further calculus help (1 Viewer)

[kr73114]

1) integrate x^3/(2-x^2)

2) if f(x)= (ax+b)sinx + (cx+d)cosx, determine the values of the constants a, b, c and d such that f'(x)=xcosx

thanks

 

[xV1P3R]

1) x³/(2-x²) = (x³ - 2x + 2x)/(2-x²) = -x + 2x/(2-x²) which should be easier to integrate

2) f(x) = axsin(x) + bsin(x) + cxcos(x) + dcos(x)

f'(x) = asin(x) + axcos(x) + bcos(x) + ccos(x) - cxsin(x) - dsin(x)

= sin(x)[a-d-cx] + cos(x)[ax + b + c]

Since you want f'(x) = xcos(x) for all x, then c = 0, a = 1, a - d = 0, b + c = 0

 

[kr73114]

thanks
how do u know what a, b, c and d are equal...i got the rest

 

[xV1P3R]

You want the coefficients of sin(x), xsin(x) and cos(x) to be 0. So if you separate it better than I did, you should be able to work it out.