Find the definite integral of the following between x = 2 and x = 6?

Question

1) #8x^3 + 20x – 2#

2) Cos(8x)

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Answer 1 · 2018-03-25T19:22:18

#2872, 1/8(sin48-sin16)#

#int_2^6(8x^3+20x-2)dx=(8/4x^4+20/2x^2-2x)|_2^6#

#=(2x^4+10x^2-2x)|_2^6=(2(1296)+10(36)-12)-(2(16)+10(4)-4)=2940-68=2872#

#int_2^6cos(8x)dx=(1/8sin(8x))|_2^6#

#=(1/8sin(48)-1/8sin(16))#