Math 108
Sample Midterm Test
1.
Evaluate
∫
(3
x
2
−4x+3−
x
−1
+2
x
−2
)dx
MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaacaGGOaGaaG4maiaadIhadaahaaWcbeqaaiaaikdaaaGccqGHsislcaaI0aGaamiEaiabgUcaRiaaiodacqGHsislcaWG4bWaaWbaaSqabeaacqGHsislcaaIXaaaaOGaey4kaSIaaGOmaiaadIhadaahaaWcbeqaaiabgkHiTiaaikdaaaGccaGGPaGaamizaiaadIhaaSqabeqaniabgUIiYdaaaa@4A60@
(
Solution)
2.
Evaluate
∫
(x−3)
(
x
2
−6x+3)
7
dx
MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaacaGGOaGaamiEaiabgkHiTiaaiodacaGGPaGaaiikaiaadIhadaahaaWcbeqaaiaaikdaaaGccqGHsislcaaI2aGaamiEaiabgUcaRiaaiodacaGGPaWaaWbaaSqabeaacaaI3aaaaOGaamizaiaadIhaaSqabeqaniabgUIiYdaaaa@4659@
(
Solution)
3.
Evaluate
∫
x
e
2
x
2
−5
dx
MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaacaWG4bGaamyzamaaCaaaleqabaGaaGOmaiaadIhadaahaaadbeqaaiaaikdaaaWccqGHsislcaaI1aaaaaqabeqaniabgUIiYdGccaWGKbGaamiEaaaa@403C@
(
Solution)
4.
Evaluate
∫
2+3lnx
x
dx
MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaadaWcaaqaaiaaikdacqGHRaWkcaaIZaGaciiBaiaac6gacaWG4baabaGaamiEaaaaaSqabeqaniabgUIiYdGccaWGKbGaamiEaaaa@4022@
(
Solution)
5.
Evaluate
∫
1
2
(
x
2
+1)
2
dx
MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qCaeaacaGGOaGaamiEamaaCaaaleqabaGaaGOmaaaakiabgUcaRiaaigdacaGGPaWaaWbaaSqabeaacaaIYaaaaOGaamizaiaadIhaaSqaaiaaigdaaeaacaaIYaaaniabgUIiYdaaaa@418D@
(
Solution)
6.
Find the area of the region bounded by the graph
of
f(x)=2
x
2
−x+3
MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacIcacaWG4bGaaiykaiabg2da9iaaikdacaWG4bWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaamiEaiabgUcaRiaaiodaaaa@406A@
,
the x-axis, the vertical lines x = -2 and x = 2.
(
Solution)
7.
Find the area of the region bounded by the graph
of
f(x)=
e
3x
MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacIcacaWG4bGaaiykaiabg2da9iaadwgadaahaaWcbeqaaiaaiodacaWG4baaaaaa@3D06@
,
the x-axis, and the vertical lines x = 0 and x = 1.
(
Solution)
8.
Find the area of the region bounded by the graph
of
f(x)=2
x
2
−3
MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacIcacaWG4bGaaiykaiabg2da9iaaikdacaWG4bWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaaG4maaaa@3E8B@
and
g(x)=x
MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4zaiaacIcacaWG4bGaaiykaiabg2da9iaadIhaaaa@3B33@
.
(
Solution)
9.
Find the area of the region bounded by the graph
of
f(x)=
x
2
−3x+2
MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacIcacaWG4bGaaiykaiabg2da9iaadIhadaahaaWcbeqaaiaaikdaaaGccqGHsislcaaIZaGaamiEaiabgUcaRiaaikdaaaa@406A@
,
the x-axis and the vertical lines x = 0 and x = 3.
(
Solution)
10.
Evaluate
∫
x
e
2x
dx
MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaacaWG4bGaamyzamaaCaaaleqabaGaaGOmaiaadIhaaaGccaWGKbGaamiEaaWcbeqab0Gaey4kIipaaaa@3DA6@
(
Solution)