Please help me: QUESTION 1 none of the above -----------------------------------

ID: 2872960 • Letter: P

Question

Please help me:

QUESTION 1

none of the above

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QUESTION 2

Use integration by parts to calculate

none of the above

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QUESTION 3

Evaluate the following trigonometric integral:

none of the above

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QUESTION 4

Use trigonometric substitution to evaluate

none of the above

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QUESTION 5

none of the above

Q1)integral e-2x cosx dx

u =cosx ,dv= e-2xdx ,du=-sinx dx,v=(-1/2) e-2x

integral u dv =uv -integral vdu

=(-1/2)cosx e-2x -integral (-1/2) e-2x*(-sinx) dx

=(-1/2)cosx e-2x -(1/2)integral e-2xsinx dx

u =sinx ,dv= e-2xdx ,du=cosx dx,v=(-1/2) e-2x

integral u dv =uv -integral vdu

=(-1/2)cosx e-2x -(1/2)[sinx(-1/2) e-2x -integral (-1/2) e-2xcosx dx]

=(-1/2)cosx e-2x -(1/2)sinx(-1/2) e-2x -integral (1/4) e-2xcosx dx

integral e-2x cosx dx=(-1/2)cosx e-2x -(1/2)sinx(-1/2) e-2x -integral (1/4) e-2xcosx dx

(1+ 1/4)integral e-2x cosx dx=(-1/2)cosx e-2x -(1/2)sinx(-1/2)e-2x +c

(5/4)integral e-2x cosx dx=(-1/2)cosx e-2x +(1/4)sinxe-2x +c

integral e-2x cosx dx=(-2/5)cosx e-2x +(1/5)sinxe-2x +C

integral e-2x cosx dx=(1/5)e-2x(-2cosx +sinx)+C

integral e-2x cosx dx=(1/5)e-2x(sinx-2cosx ) +C

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