Ben asked in Science & MathematicsMathematics · 2 months ago

Calculus Help?

Ive been having some trouble solving these problems. Any help would be absolutely appreciated.

Update:

I figured out #3.

Update 2:

Figured out 1 & 3.

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  • 2 months ago

    1) The problem is Int(x*sin2x)dx

    Integrate by parts

    Int(u *dv) = uv - int(v * du)

    We need to indentify the parts now.

    u = x

    dv = sin2x

    v = int(sin2x)dx = -1/2 * cos(2x)

    du =1

    Now plug it all into the equation Int(u *dv) = uv - int(v * du)

    Int(x*sin2x)dx = -1/2*x*cos(2x) - int(-1/2 *cos(2x))

                           = -1/2*x*cos(2x) + 1/4 sin(2x)

                           =1/4(sin(2x) - 2x*cos(2x)) + c

    I think I did this right

    2) I'm not really sure how to do this, it's been too long

    3) Int((x-6)/(x(x-3)) dx

    First, simplify the integrand using partial fraction decomposition, and you end up with

    Int(2/x - 1/(x-3))dx

    = Int(2/x) dx - Int((x-3)^-1)dx

    = 2 Int x^-1 dx - int ((x-3)^-1)dx

    = 2 ln x - ln (x-3) + c

    4) Not quite sure

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