# NCERT Solutions Class 12 Maths Chapter-7 (Integrals)Exercise 7.9

NCERT Solutions Class 12 Maths from class 12th Students will get the answers of Chapter-7 (Integrals)Exercise 7.9 This chapter will help you to learn the basics and you should expect at least one question in your exam from this chapter.
We have given the answers of all the questions of NCERT Board Mathematics Textbook in very easy language, which will be very easy for the students to understand and remember so that you can pass with good marks in your examination.

### Exercise 7.9

Q1. Evaluate the definite integral :

Answer.  By second fundamental theorem of calculus , we obtain $I=\mathrm{F}\left(1\right)-\mathrm{F}\left(-1\right)$

Q2. Evaluate the definite integral : ${\int }_{x}^{1}\frac{1}{x}dx$

Answer.  By second fundamental theorem of calculus , we obtain

Q3. Evaluate the definite integral : ${\int }^{2}\left(4{x}^{3}-5{x}^{2}+6x+9\right)dx$

Answer.  By second fundamental theorem of calculus , we obtain

Q4. Evaluate the definite integral : ${\int }_{0}^{x}\mathrm{sin}2xdx$

Answer.  By second fundamental theorem of calculus , we obtain

Q5. Evaluate the definite integral :

Answer.  By second fundamental theorem of calculus , we obtain

Q6. Evaluate the definite integral :

Answer.  By second fundamental theorem of calculus , we obtain

Q7. Evaluate the definite integral :

Answer.  By second fundamental theorem of calculus , we obtain

Q8. Evaluate the definite integral :

Answer. $I={\int }_{\pi }^{\frac{\pi }{4}}\mathrm{cos}\mathrm{ec}xdx$ $\int \mathrm{csc}xdx=\mathrm{log}|\mathrm{csc}x-\mathrm{cot}x|=\mathrm{F}\left(x\right)$ By second fundamental theorem of calculus , we obtain

Q9. Evaluate the definite integral : ${\int }_{0}^{4}\frac{dx}{\sqrt{1-{x}^{2}}}$

Answer.  By second fundamental theorem of calculus , we obtain

Q10. Evaluate the definite integral : $\int \frac{dx}{1+{x}^{2}}$

Answer.  By second fundamental theorem of calculus , we obtain

Q11. Evaluate the definite integral : ${\int }_{2}^{3}\frac{dx}{{x}^{2}-1}$

Answer.  By second fundamental theorem of calculus , we obtain

Q12. Evaluate the definite integral :

Answer.  By second fundamental theorem of calculus , we obtain

Q13. Evaluate the definite integral :

Answer.  By second fundamental theorem of calculus , we obtain

Q14. Evaluate the definite integral : $\int \frac{2x+3}{5{x}^{2}+1}dx$

Answer. $I={\int }_{0}^{4}\frac{2x+3}{5{x}^{2}+1}dx$