Determine the following definite integrals: \int_{-1}^{3}|2x-x^{2}|dx

aflacatn 2021-09-16 Answered
Determine the following definite integrals:
13|2xx2|dx
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Expert Answer

avortarF
Answered 2021-09-17 Author has 113 answers
Step 1
Evaluate the integrals:
f(x)=13|2xx2|dx
Eliminate the absolutes,
1x0 f(x)=(2x+x2)
0x2 f(x)=(2xx2)
2x3 f(x)=(2x+x2)
f(x)=10(2x+x2)dx+02(2xx2)dx+23(2x+x2)dx
=[2(x22)+x33]10+[2(x22)x33]02+[2(x22)+x33]23
=[x2+x33]10+[x2x33]02+[x2+x33]23
=[0((1)2+(1)33)]+[222330]+[(32+333)(22+233)]
Jeffrey Jordon
Answered 2021-11-08 Author has 2027 answers

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