How do you evaluate #\int _ { 5} ^ { 10} x \sin 10d x#?

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Answer 1 · 2017-06-28T13:06:36

We want to evaluate:

# int _5^10 \ x sin10 \ dx = 75/2sin10 #

We want to evaluate:

# I = int _5^10 \ x sin10 \ dx #

As #sin10# is a constant we have:

# I = sin10 \ int _5^10 \ x \ dx #

Then using the power rule for integral calculus we have:

# I = sin10 \ [ x^2/2 ]_5^10#
# \ \ = sin10 \ 1/2 \ [ x^2 ]_5^10#
# \ \ = (1/2sin10 )(100-25)#
# \ \ = (1/2sin10) (75)#
# \ \ = 75/2sin10#