Students can Download Basic Maths Exercise 20.2 Questions and Answers, Notes Pdf, 2nd PUC Basic Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

## Karnataka 2nd PUC Basic Maths Question Bank Chapter 20 Indefinite Integrals Ex 20.2

Part-A

**2nd PUC Basic Maths Indefinite Integrals Ex 20.2 Three and Five Marks Questions and Answers**

Question 1.

(7x – 3)^{4}

Answer:

Question 2.

\((2 x+5)^{\frac{3}{2}}\)

Answer:

\(\int(2 x+5)^{\frac{3}{2}} d x=\frac{(2 x+5)^{\frac{3}{2}+1}}{\left(\frac{3}{2}+1\right) \cdot 2}=\frac{(2 x+5)^{\frac{5}{2}}}{5}+C\)

Question 3.

\(\frac{1}{10 x+3}\)

Answer:

Question 4.

e^{3 – 4x}

Answer:

\(\int e^{3-4 x} d x=\frac{e^{3-4 x}}{-4}+C\)

Question 5.

3^{5x – 3}

Answer:

\(\int 3^{5 x-3} \cdot d x=\frac{3^{5 x-3}}{5 \cdot \log 3}+C\)

Question 6.

sec^{2}(x – 5)

Answer:

∫sec^{2}(x – 5)dx = tan(x – 5) + c

Question 7.

cosec(3 – 5x) cot (3 – 5x)

Answer:

\(\int \csc (3-5 x) \cdot \cot (3-5 x) d x=-\frac{\csc (3-5 x)}{-5}+C\)

Part-B

**2nd PUC Basic Maths Indefinite Integrals Ex 20.2 Two Marks Questions and Answers**

Question 1.

cos^{2}

Answer:

\(\int \cos ^{2} x \cdot d x=\int \frac{1+\cos 2 x}{2} d x=\frac{1}{2}\left[x+\frac{\sin 2 x}{2}\right]+C\)

Question 2.

cot^{2}(5x + 3).

Answer:

∫cot^{2}(5x + 3)dx = ∫cosec^{2}(5x + 3)-1)dx = \(\frac{\cot (5 x+3)}{5}\) -x + c.

Question 3.

cos^{3}x

Answer:

Question 4.

(3x + 4)^{3} + 5^{7 – 3x}.

Answer:

Part-C

**2nd PUC Basic Maths Indefinite Integrals Ex 20.2 Three Marks Questions and Answers**

Question 1.

sin 2x cos 3x

Answer:

∫sin 2x . cos 3x dx = ∫\(\frac { 1 }{ 2 }\)[sin 5x – sin x] dx (using transformation formula)

\(=\frac{1}{2}\left[\frac{-\cos 5 x}{5}+\cos x\right]+C\)

Question 2.

cos 9x sin 4x.

Answer:

∫cos 9x . sin 4x . dx (using ttransformation formula)

= ∫\(\frac { 1 }{ 2 }\)(sin 13x – sin 5x)dx

\(=\frac{1}{2}\left[\frac{-\cos 13 x}{13}+\frac{\cos 5 x}{5}\right]+C\)

Question 3.

cos 7x cos 6x

Answer:

∫cos 7x . cos 6x . dx

= ∫\(\frac { 1 }{ 2 }\) (cos 13x + cos x ) dx

\(=\frac{1}{2}\left[\frac{\sin 13 x}{13}+\sin x\right]+C\)

Question 4.

sin 11x sin 7x.

Answer:

∫sin 11x . sin 7x .dx = –\(\frac { 1 }{ 2 }\)∫cos 18x – cos 4x . dx

\(=-\frac{1}{2}\left[\frac{\sin 18 x}{18}-\frac{\sin 4 x}{4}\right]\)

\(=\frac{\sin 4 x}{8}-\frac{\sin 18 x}{36}+C\)

Question 5.

\(\int \frac{x}{\sqrt{x-5}}\)

Answer:

Question 6.

\(\frac{2 x}{2 x+3}\)

Answer:

Question 7.

\(\frac{3 x}{5 x-1}\)

Answer:

Question 8.

\(\frac{2 x+5}{3 x+4}\)

Answer:

Part-D

**2nd PUC Basic Maths Indefinite Integrals Ex 20.2 Four Marks Questions and Answers**

Question 1.

\(\sqrt{1+\sin x}\)

Answer:

Question 2.

\(\int \frac{1}{1-\cos x} d x\)

Answer:

Question 3.

\(\frac{1}{\sqrt{x}-\sqrt{2+x}}\)

Answer:

Question 4.

\(\frac{4}{\sqrt{x+1}+\sqrt{x+2}}\)

Answer:

Question 5.

\(\frac{5}{\sqrt{3 x+1}-\sqrt{3 x+4}}\)

Answer: