Perform the integration. integral 4 cos^3 x sin^6 x dx 4/7 (sin^7 x - sin^9 x) +
ID: 2878458 • Letter: P
Question
Perform the integration. integral 4 cos^3 x sin^6 x dx 4/7 (sin^7 x - sin^9 x) + C 4/5 cos^5 x - 4/7 cos^7 x + C 4/5 sin^5 x - 4/9 cos^9 x + C 4/7 sin^7 x - 4/9 sin^9 x + C integral dx/squareroot -x^2 + 8x + 9 1/5 tan^-1 (x - 4/5) + C sin^-1 (x + 4/5) + C sin^-1 (x + 4/5) + C sin^-1 (x - 8/5) + C Find the volume of the solid generated by revolving the region bounded by the curve y = ln x, x-axis, and the vertical line x = e^2 about the x-axis. pi(e - 1) pi e pi(e^2 - 1) 2pi(e^2 - 1) Use integration by parts to evaluate the integral. integral (x^2 - 8x)e^x dx 1/3 x^3 e^x - 4x^2 e^x + C e^x [x^2 - 10x - 10] + C e^x[x^2 - 10x + 10] + C e^x [x^2 - 8x + 8] + C Set up an integral for the length of the curve. x = sin 2y, -pi lessthanorequalto y lessthanorequalto 0 integral_-pi^0 squareroot 1 + 4 cos^2 2y dy integral_-pi^0 squareroot 1 + 4 sin^2 2y dy integral_-pi^0 squareroot 1 + 2 cos 2y dy integral_-pi^0 squareroot 1 + cos^2 2y dy Use the substitution formula to evaluate the integral. integral_0^1 6x dx/squareroot 16 + 3r^2 squareroot 19/2 - 2 squareroot 19 - 4 2 squareroot 19 - 8 -2 squareroot 19 + 8Explanation / Answer
12)4cos3xsin6x dx
=4cos2xsin6x cosx dx
=4(1-sin2x)sin6x cosx dx
=4(sin6x-sin8x) cosx dx
=4((1/7)sin7x-(1/9)sin9x) +C
=(4/7)sin7x-(4/9)sin9x +C
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13)dx/(-x2+8x+9)
=dx/(9-(x2-8x))
=dx/(9-(x2-8x+16-16))
=dx/(9+16-(x2-8x+16))
=dx/(25-(x-4)2)
=dx/(25(1-((x-4)2)/25))
=dx/(25(1-((x-4)/5)2))
=dx/5(1-((x-4)/5)2)
substitute (x-4)/5=sinu => u=sin-1((x-4)/5)
(x-4)=5sinu
differentiate => dx -0 =5cosu du => dx =5cosu du
=5cosu du/5(1-(sinu)2)
=5cosu du/5cosu
=du
=u+c
=sin-1((x-4)/5) +C