Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12

Students can download 12th Business Maths Chapter 2 Integral Calculus I Ex 2.12 Questions and Answers, Samacheer Kalvi 12th Business Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12

Choose the correct answer.

Question 1.
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q1
Answer:
(b) \(\frac{-1}{2 x^{2}}+c\)
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q1.1

Question 2.
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q2
Answer:
(c) \(\frac{2^{x}}{\log 2}+c\)

Question 3.
\(\int \frac{\sin 2 x}{2 \sin x} d x\) is _______
(a) sin x + c
(b) \(\frac {1}{2}\) sin x + c
(c) cos x + c
(d) \(\frac {1}{2}\) cos x + c
Answer:
(a) sin x + c
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q3

Question 4.
\(\int \frac{\sin 5 x-\sin x}{\cos 3 x} d x\) is _____
(a) -cos 2x + c
(b) –\(\frac {1}{2}\) cos 2x + c
(c) \(-\frac{1}{4}\) cos 2x + c
(d) -4 cos 2x + c
Answer:
(a) -cos 2x + c
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q4

Question 5.
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q5
Answer:
(a) \(\frac{1}{2}(\log x)^{2}\)
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q5.1

Question 6.
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q6
Answer:
(b) \(2 \sqrt{1+e^{x}}+c\)
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q6.1

Question 7.
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q7
Answer:
(b) \(2 \sqrt{e^{x}}+c\)
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q7.1

Question 8.
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q8
Answer:
(a) \(e^{2 x} x^{2}+c\)
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q8.1

Question 9.
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q9
Answer:
(d) \(\log \left|e^{x}+1\right|+c\)
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q9.1

Question 10.
\(\int\left[\frac{9}{x-3}-\frac{1}{x+1}\right] d x\) is _____
(a) log|x – 3| – log|x + 1| + c
(b) log|x – 3| + log|x + 1| + c
(c) 9log|x – 3| – log|x + 1| + c
(d) 91og|x – 3| + log|x + 1| + c
Answer:
(c) 9log|x – 3| – log|x + 1| + c

Question 11.
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q11
Answer:
(b) \(\frac{1}{2} \log \left|4+x^{4}\right|+c\)
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q11.1

Question 12.
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q12
Answer:
(b) \(\log |x+\sqrt{x^{2}-36}|+c\)
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q12.1

Question 13.
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q13
Answer:
(b) \(2 \sqrt{x^{2}+3 x+2}+c\)
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q13.1

Question 14.
\(\int_{0}^{1}(2 x+1) d x\) is _______
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(b) 2
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q14

Question 15.
\(\int_{2}^{4} \frac{d x}{x}\) is _______
(a) log 4
(b) 0
(c) log 2
(d) log 8
Answer:
(c) log 2
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q15

Question 16.
\(\int_{0}^{\infty} e^{-2 x} d x\) is _____
(a) 0
(b) 1
(c) 2
(d) \(\frac{1}{2}\)
Answer:
(d) \(\frac{1}{2}\)
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q16

Question 17.
\(\int_{-1}^{1} x^{3} e^{x^{4}} d x\) is _______
(a) 1
(b) \(2 \int_{0}^{1} x^{3} e^{x^{4}} d x\)
(c) 0
(d) 2
Answer:
(c) 0
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q17

Question 18.
If f(x) is a continous function and a < c < b, then \(\int_{a}^{c} f(x) d x+\int_{c}^{b} f(x) d x\) is _____
(a) \(\int_{a}^{b} f(x) d x-\int_{a}^{c} f(x) d x\)
(b) \(\int_{a}^{c} f(x) d x-\int_{a}^{a} f(x) d x\)
(c) \(\int_{a}^{b} f(x) d x\)
(d) 0
Answer:
(c) \(\int_{a}^{b} f(x) d x\)

Question 19.
The value of \(\int_{\frac{\pi}{2}}^{\frac{\pi}{2}} \cos x d x\) is _______
(a) 0
(b) 2
(c) 1
(d) 4
Answer:
(b) 2
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q19

Question 20.
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q20
Answer:
(a) \(\frac{1}{12}\)
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q20.1

Question 21.
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q21
Answer:
(b) 0
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q21.1

Question 22.
The value of \(\int_{2}^{3} f(5-x) d x-\int_{2}^{3} f(x) d x\) is _______
(a) 1
(b) 0
(c) -1
(d) 5
Answer:
(b) 0
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q22

Question 23.
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q23
Answer:
(c) \(\frac{28}{3}\)
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q23.1

Question 24.
\(\int_{0}^{\frac{\pi}{3}} \tan x d x\) is _______
(a) log 2
(b) 0
(c) log√2
(d) 2 log 2
Answer:
(a) log 2
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q24

Question 25.
Using the factorial representation of the gamma function, which of the following is the solution for the gamma function Γ(n) when n = 8 is _______
(a) 5040
(b) 5400
(c) 4500
(d) 5540
Answer:
(a) 5040
Hint:
Γ(8) = Γ(7 + 1) = 7! = 5040

Question 26.
Γ(n) is _____
(a) (n – 1)!
(b) n!
(c) n Γ(n)
(d) (n – 1) Γ(n)
Answer:
(a) (n – 1)!
Hint:
Γ(n) = Γ(n – 1) + 1 = (n – 1)!

Question 27.
Γ(1) is ______
(a) 0
(b) 1
(c) n
(d) n!
Answer:
(b) 1
Hint:
Γ(1) = (1 – 1)! = 0! = 1

Question 28.
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q28
Answer:
(d) \(\int_{0}^{\infty} e^{-x} x^{n-1} d x\)

Question 29.
Γ(\(\frac{3}{2}\)) is _____
(a) √π
(b) \(\frac{\sqrt{\pi}}{2}\)
(c) 2√π
(d) \(\frac{3}{2}\)
Answer:
(b) \(\frac{\sqrt{\pi}}{2}\)
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q29

Question 30.
\(\int_{0}^{\infty} x^{4} e^{-x} d x\) is _______
(a) 12
(b) 4
(c) 4!
(d) 64
Answer:
(c) 4!
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.12 Q30

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