Mathematics Questions and Answers – Definite Integral

«
»

This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Definite Integral”.

1. In \(\int_a^b\)f(y) dy, what is ‘a’ called as?
a) Integration
b) Upper limit
c) Lower limit
d) Limit of an integral
View Answer

Answer: b
Explanation: In \(\int_a^b\)f(y) dy ‘a’ is the called as lower limit and ‘b’ is called the upper limit of the integral. The fuction f in \(\int_a^b\)f(y) dy is called the integrand. The letter ‘y’ is a dummy symbol and can be replaced by any other symbol.
advertisement

2. The value of \(\int_0^{\pi }\)sin ⁡y dy is 2.
a) True
b) False
View Answer

Answer: a
Explanation: \(\int_0^{\pi }\)sin⁡ y dy = [-cos y]y0
= – cos π – (- cos 0)
= -(-1)-(-1)
= 2

3. Compute ∫cos(x)-\(\frac {3}{x4}\)dx.
a) sin(x)+\(\frac {3}{4}\)x-7+c
b) sec(x)+\(\frac {3}{4}\)x-3+c
c) sin(x)+\(\frac {3}{4}\)x-3
d) sin(x)+\(\frac {3}{4}\)x-3+c
View Answer

Answer: d
Explanation: ∫cos(x)-\(\frac {3}{x4}\)dx = ∫cos(x) dx−∫3(x-4) dx
= sin(x)+\(\frac {3}{4}\)x-3+c
advertisement
advertisement

4. What is the value of \(\int_2^3\)cos⁡(x)-\(\frac {3}{x4}\)dx .
a) sin (3) – sin (2)
b) sin (3) – sin (9) – \(\frac {19}{288}\)
c) sin (8) – sin (2) – \(\frac {19}{288}\)
d) sin (3) – sin (2) – \(\frac {19}{288}\)
View Answer

Answer: d
Explanation: \(\int_2^3\)cos⁡(x)-\(\frac {3}{x4}\)dx = \(\int_2^3\)sin(x) dx + \(\int_2^3 \frac {3}{4}\)x-3 dx
= (sin (3) + \(\frac {3}{4}\)3-3) – (sin (2) + \(\frac {3}{4}\)2-3)
= sin (3) – sin (2) – \(\frac {19}{288}\)

5. Evaluate \(\int_7^9\)cos⁡(x)dx.
a) 8 (-sin 9 – sin 7)
b) 8 (sin 9 + sin 7)
c) 8 (sin 9 – sin 7)
d) 7 (sin 9 – sin 7)
View Answer

Answer: c
Explanation: \(\int_7^9\)8cos⁡(x)dx = 8 \(\int_7^9\)cos⁡(x)dx
= 8 (cos x)97
= 8 (sin 9 – sin 7)
advertisement

6. Compute \(\int_2^3 \frac {cos⁡x-sin⁡x}{4}\)dx.
a) \(\frac {1}{4}\) (sin 2 + cos 3 – sin 3 – cos 2)
b) \(\frac {1}{4}\) (sin 3 – cos 3 – sin 2 – cos 2)
c) \(\frac {1}{4}\) (sin 3 + cos 3 – sin 2 – cos 2)
d) \(\frac {1}{4}\) (sin 3 + cos 3 + sin 2 – cos 2)
View Answer

Answer: c
Explanation: \(\int_2^3 \frac {cos⁡x-sin⁡x}{4}\)dx = \(\frac {1}{4}\) [sin x – (- cos x)]32
= \(\frac {1}{4}\) (sin x + cos x)32
= \(\frac {1}{4}\) (sin 3 + cos 3) – \(\frac {1}{4}\) (sin 2 + cos 2)
= \(\frac {1}{4}\) (sin 3 + cos 3 – sin 2 – cos 2)

7. What is y in \(\int_a^b\)f(y) dy called as?
a) Random variable
b) Dummy symbol
c) Integral
d) Integrand
View Answer

Answer: b
Explanation: In \(\int_a^b\)f(y) dy ‘a’ is the called as lower limit and ‘b’ is called the upper limit of the integral. The fuction ‘f’ in \(\int_a^b\)f(y) dy is called the integrand. The letter ‘y’ is a dummy symbol and can be replaced by any other symbol.
advertisement

8. The value of \(\int_1^2\)1y5 dy is_____
a) 10.5
b) 56
c) 9
d) 23
View Answer

Answer: a
Explanation: \(\int_1^2\)1y5 dy = (y6/6)21
= \(\frac {64}{6} – \frac{1}{6}\)
= 10.5

9. The value of \(\int_1^2\)1y5/5dy is _____
a) 12
b) 2.1
c) 21
d) 11.1
View Answer

Answer: b
Explanation: \(\int_1^2\)1y5/5dy = \(\frac {1}{5}\)(y6/6)21
= \(\frac {1}{5}(\frac {64}{6} – \frac{1}{6})\)
= 2.1
advertisement

10. Evaluate \(\int_0^{\pi }\)sin⁡x dx.
a) 2
b) 6
c) 17
d) 3
View Answer

Answer: a
Explanation: \(\int_0^{\pi }\)sin⁡x dx = [- cos x]x0
= – cos π – (-cos 0)
= -(-1)-(-1)
= 2

11. Evaluate \(\int_2^3\)cosx dx.
a) 38.2
b) sin (9) – sin (4)
c) 89.21
d) sin (3) – sin (2)
View Answer

Answer: d
Explanation: \(\int_2^3\)cosx dx = (sin x)32
= sin (3) – sin (2)

12. Compute \(\int_2^3\)2ex dx.
a) 2(e9 – e4)
b) 84.32
c) 2(e3 – e2)
d) 83.25
View Answer

Answer: c
Explanation: \(\int_2^3\)2ex dx = 2(ex)32 dx
= 2(e3 – e2)

13. In \(\int_b^a\)f(x) dx, b called as lower limit and a is called as upper limit.
a) False
b) True
View Answer

Answer: b
Explanation: In \(\int_a^b\)f(y) dy ‘a’ is the called as lower limit and ‘b’ is called the upper limit of the integral. The fuction ‘f’ in \(\int_a^b\)f(y) dy is called the integrand. The letter ‘y’ is a dummy symbol and can be replaced by any other symbol.

14. Compute \(\int_3^6\)9 ex dx.
a) 30.82
b) 9(e6 – e3)
c) 11.23
d) 81(e6 – e3)
View Answer

Answer: b
Explanation: \(\int_3^6\)9 ex dx = 9(ex)63 dx
= 9(e6 – e3)

15. Evaluate \(\int_3^7\)sin(t)-2cos(t)dt.
a) cos(7) – 2sin(7) + (cos(3) + 2sin(3)
b) -17
c) 12
d) cos(7) – 2sin(7) – (cos(3) + 2sin(3)
View Answer

Answer: d
Explanation: \(\int_3^7\)sin(t)-2cos(t)dt = (cos(t)−2sin(t))73
= (cos(7) – 2sin(7)) – (cos(3) – 2sin(3))
= cos(7) – 2sin(7) – (cos(3) + 2sin(3)

Sanfoundry Global Education & Learning Series – Mathematics – Class 12.

To practice all areas of Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.

Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

advertisement
advertisement
Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter