MTH102: Elementary Mathematics Ii TMA3

 

Question 1 : Integrate∫(x3+3×2+2x+4)
A.x42−x3+x2+4x+c
B.6×4−3×2+c
C.x44+x3+x2+4x+c
D.3×44+2×3+x+c

 

Question 2 : Given f(x) =(7×4−5×3), evaluate df(x)dx
A.28×3−15×2
B.2×3−15×2
C.28×2−15×2
D.7×4−5×3

Answer to question 2 is A. A.28×3−15×2

Question 3 : Evaluate∫e4xdx
A.ex+c
B.13ex+c
C.14e4x+c
D.3ex3+c

Answer to question 3. Is A. ex+c

Question 4 : Find∫sec3xtanxdx
A.cos3x2+c
B.sin2x+c
C.cos2x+c
D.sec3x3+c

Answer to question 4. Is A. ex

Question 5 : Find the volume of a sphere generated by a semicircley=√(r2−x2) revolving around the x-axis
A.4πr32
B.4πr33
C.−π−r32
D.πr34

 

Question 6 : Find the integral with respect to x∫cosxsinxdx
A.cos2x2+c
B.sinx
C.sin2x2+c
D.sin2x+c

 

Question 7 : Find the∫tan3xsec3xdx
A.sec2x+1
B.cot2x+1
C.sec2x
D.tan2x+1

 

Question 8 : Integrate with respect to x :∫3−1x√7+x2dx
A.4−2√2
B.2√2
C.√2
D.4√2

 

Question 9 : Evaluate∫3ex+5cos(x)−10sec2(x)dx
A.2ex−x−10tanx+c
B.3e2+5sinx−10tanx+c
C.3ex+cosx−10tanx+c
D.3ex+5sinx−10secx+c

 

Question 10 : Evaluate∫x2e3xdx
A.e3x3(x2−2×3+29)+c
B.ex3(x2+2×3−25)+c
C.e2x3(x3−x4+29)+c
D.−e3x3(x2+2×3−29)+c

 

Question 11 : Evaluate∫x+1×2−3x+2dx
A.3ln(x−2)−2ln(x−1)+c
B.3ln(x−2)+2ln(x+1)+c
C.3ln(x+2)−2ln(x+1)+c
D.−3ln(x−2)−2ln(x−1)+c

 

Question 12 : Integrate with respect to x :∫2−1×2(x3+4)2dx
A. 6
B.12
C. 12
D.512

 

Question 13 : Evaluate∫2−1y2+y−2dy
A.716
B.316
C.516
D.1716

 

Question 14 : Evaluate∫(3x−2)6dx
A.(3x+2)72+c
B.(3x−2)721+c
C.(3x+2)721+c
D.3(3x−2)72+c

 

Question 15 : Evalute∫x2(3−10×3)dx
A.115(3−20×3)5)+c
B.110(1−10×2)5)+c
C.1150(3−10×3)5)+c
D.1100(3−2×3)5)+c

 

Question 16 : Find∫xcosax2dx with respect to x
A.12asinax2+c
B.sec2x+1
C.sin2x+c
D.cos3x+c

 

Question 17 : Determine∫x2+1(x+2)3
A.ln(x+2)+4x+2−52(x+3)2+c
B.ln(x−2)+4x−2−52(x+3)2+c
C.ln(x+2)−4x+2−52(x+3)2+c
D.−ln(x+2)−4x+2−52(x+3)2+c

 

Question 18 : Integrate with respect to x :∫41x+1√xdx
A. -20
B.203
C.320
D. 20

 

Question 19 : Evaluate∫cos(6x+4)dx
A.sin(6x+4)6+c
B.tan(6x+4)6+c
C.cos(6x+4)6+c
D.sec(6x+4)6+c

 

Question 20 : Evaluate∫xe6xdx
A.x6e6x−1136e6x+c
B.x3e6x+116e6x+c
C.x6e6x+1136e6x+c
D.−x6e6x+1136e6x+c