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.

Answer:
(b) $$\frac{-1}{2 x^{2}}+c$$
Hint:

Question 2.

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:

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:

Question 5.

Answer:
(a) $$\frac{1}{2}(\log x)^{2}$$
Hint:

Question 6.

Answer:
(b) $$2 \sqrt{1+e^{x}}+c$$
Hint:

Question 7.

Answer:
(b) $$2 \sqrt{e^{x}}+c$$
Hint:

Question 8.

Answer:
(a) $$e^{2 x} x^{2}+c$$
Hint:

Question 9.

Answer:
(d) $$\log \left|e^{x}+1\right|+c$$
Hint:

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.

Answer:
(b) $$\frac{1}{2} \log \left|4+x^{4}\right|+c$$
Hint:

Question 12.

Answer:
(b) $$\log |x+\sqrt{x^{2}-36}|+c$$
Hint:

Question 13.

Answer:
(b) $$2 \sqrt{x^{2}+3 x+2}+c$$
Hint:

Question 14.
$$\int_{0}^{1}(2 x+1) d x$$ is _______
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(b) 2
Hint:

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:

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:

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:

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:

Question 20.

Answer:
(a) $$\frac{1}{12}$$
Hint:

Question 21.

Answer:
(b) 0
Hint:

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:

Question 23.

Answer:
(c) $$\frac{28}{3}$$
Hint:

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:

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.

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:

Question 30.
$$\int_{0}^{\infty} x^{4} e^{-x} d x$$ is _______
(a) 12
(b) 4
(c) 4!
(d) 64
Answer:
(c) 4!
Hint: