Home
Class 11
MATHS
Evaluate the following : (i) int sqrt(...

Evaluate the following :
`(i) int sqrt(4 - x^2) dx " " (ii) int sqrt(25 x^2 - 9)dx " " (iii) int sqrt(x^2 + x + 1) dx`.

Text Solution

Verified by Experts

The correct Answer is:
(i) `x/2 sqrt(4 - x^2) + 2 sin^(-1)(x/2) + c`.
(ii) `1/5[(5x)/2 sqrt(25 x^2 - 9) - 9/2 log |5x + sqrt(25x^2 - 9)|]+c`.
(iii) `(2x + 1)/(4) sqrt(x^2 + x + 1) + 3/8 log |x + 1/2 + sqrt(x^2 + x + 1)|+c`
Promotional Banner

Topper's Solved these Questions

  • INTEGRAL CALCULUS

    FULL MARKS|Exercise ADDITIONAL PROBLEMS|59 Videos

  • INTEGRAL CALCULUS

    FULL MARKS|Exercise EXERCISE 11.1|4 Videos

  • EXAMINATION QUESTION PAPER MARCH 2019

    FULL MARKS|Exercise MATHEMATICS|49 Videos

  • INTRODUCTION TO PROBABILITY THEORY

    FULL MARKS|Exercise ADDITIONAL PROBLEM|17 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following: int(x^(2))/(sqrt(1-x))dx

Evaluate the following: int sqrt(1+sin((1)/(2)x))dx

Evaluate the following integrals. (i) int 1/((x - 2)^2 + 1)dx " " (ii) int (x^2)/(x^2 + 5)dx " " (iii) int 1/(sqrt(1 + 4x)^2)dx

Evaluate the following integrals: (i) int 2x sqrt(1 + x^2)dx " " (ii) int e^(-x^2) x dx " " (iii) int (sin x)/(1 + cos x) dx (iv) int 1/(1 + x^2)dx " " (v) int x (a - x)^8 dx .

Evaluate the following with respect to x. (i) int (4x + 5)^6 dx " " (ii) int sqrt((15 - 2x))dx " " (iii) int 1/((3x + 7)^4) dx .

Evaluate the following integrals. (i) int 1/(x^2 - 2x + 5)dx " " (ii) int 1/(sqrt(x^2 + 12x + 11))dx .

int sqrt(1-cos2x) dx= …………

int sqrt((1 - x)/(1 + x )) dx is

Find the following integrals int(1-x)sqrt(x)dx

Evaluate the following integrals. int(sqrt(x)+(1)/(sqrt(x)))dx