Home
Class 12
MATHS
P rov et h a t4lt=int1^3sqrt(3+x^2)lt=4s...

`P rov et h a t4lt=int_1^3sqrt(3+x^2)lt=4sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
NA

Since `1lexle3`
or `1lex^(2)le9`
or `4lex^(2)+3le12`
or `2lesqrt(3+x^(2))le2sqrt(3)`
or `2(3-1)leint_(1)^(3)sqrt(3+x^(2))dx le 2sqrt(3)(3-1)`
or `4le int_(1)^(3)sqrt(3+x^(2))le 4 sqrt(3)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.4|10 Videos
  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.5|11 Videos
  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.2|17 Videos
  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos
  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

P rov et h a t1/2lt=int_0^(1/2)(dx)/(sqrt(1-x^(2n)))lt=pi/6forngeq1.

int(1)/(sqrt(3+4x))dx=

(1)/(sqrt(x+3)-sqrt(x-4))

The equation sin^4x-2cos^2x+a^2=0 can be solved if (a) -sqrt(3)lt=alt=sqrt(3) (b) sqrt(2)lt=alt=""sqrt(2) (c) -""1lt=alt=a (d) none of these

Evaluate: int1/(sqrt(3x+4)-sqrt(3x+1))dxdot

Prove that pi/6 lt int_0^1(dx) /(sqrt(4-x^2-x^3)) lt pi/(4sqrt(2))

A curve is given by b yy={(sqrt(4-x^2)),0lt=x<1sqrt((3x)),1lt=xlt=3. Find the area lying between the curve and x-axis.

Prove that sin^(-1). ((x + sqrt(1 - x^(2))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)

Evalute int(1)/(sqrt(x+3)-sqrt(x-4))dx.

Show that int_(3)^(4)(sqrt(x))/(sqrt(7-x)+sqrt(x))dx=(1)/(2)