Evaluate the following integrals. \int_{-2}^{-1}\sqrt{-4x-x^{2}}dx

York 2021-02-12 Answered
Evaluate the following integrals.
214xx2dx
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Expert Answer

yagombyeR
Answered 2021-02-13 Author has 92 answers
Step 1: Given that
214xx2dx
Step 2: Formula Used
a2x2=x2a2x2+a22sin1(xa)+C
Step 3: Solve
We have,
214xx2dx=21(4x+x2)dx
=21(4x+x2+44)dx
=21((x+2)24)dx
=214(x+2)2dx
=21(2)2(x+2)2dx
=[x+224(x+2)2+42sin1(x+22)]21
=[1+224(1+2)2+2sin1(1+22)2+224(2+2)2=2sin1(2+22)]
=[1241+2sin1(12)00]
=32+2sin1(sinπ6)
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