Home
Class 12
MATHS
Ifint(pi/3)^xsqrt((3-sin^2t))dt+int0^yco...

`Ifint_(pi/3)^xsqrt((3-sin^2t))dt+int_0^ycostdt=0,t h e ne v a l u a t e(dy)/(dx)`

Text Solution

Verified by Experts

The correct Answer is:
`(-sqrt(3)-sin^(2)x)/(cosy)`
We have `int_(pi//3)^(x)(sqrt(3-sin^(2)t))dt+int_(0)^(y)costdt=0`
Differentiating w.r.t `x`
`d/(dx) int_(pi//3)^(x)sqrt((3-sin^(2)t))dt+d/(dx)int_(0)^(y)cos dt =0`
or `sqrt((3-sin^(2)x))+cosy(dy)/(dx)=0`
or `(dy)/(dx)=(sqrt((3-sin^(2)x)))/(cosy)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.10|7 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.11|6 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.8|7 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

If int_((pi)/(3))^(x)sqrt((3-sin^(2)t))dt+int_(0)^(y)cos tdt=0, then evaluate (dy)/(dx)

If int_(0)^(y)e^(-t^(2))dt+int_(0)^(x^(2))sin^(2)tdt=0 , then (dy)/(dx) at x=y=1 is

If int_(y)^(y)cos t^(2)dt=int_(0)^(x^(2))(sin t)/(t)dx, the prove that (dy)/(dx)=(2sin x^(2))/(x cos y^(2))

Find the derivative (dy)/(dx) of the following implicit functions : (a) int_(0)^(y) e^(-t^(2)) dt + int_(0)^(x^(3)) sin ^(2) t dt = 0 (b) int_(0)^(y) e^(t) dt + int _(0)^(x) sin t dt = 0 (c) int _(pi//2)^(x) sqrt(3 - 2 sin^(2)z ) dz + int_(0)^(y) cos t dt = 0

If (d)/(dx)(int_(0)^(y)e^(-t^(2))dt+int_(0)^(x^(2)) sin^(2) tdt)=0, "find" (dy)/(dx).

If int _(0) ^(y) cos t ^(2) dt= int _(0) ^(x ^(2)) (sint)/(t ) dt then (dy)/(dx) is equal to

If f(x)= int_(0^(sinx) cos^(-1)t dt +int_(0)^(cosx) sin^(-1)t dt, 0 lt x lt (pi)/(2) then f(pi//4) is equal to

If int_(0)^(1)(e^(t))/(1+t)dt=a, then find the value of int_(0)^(1)(e^(t))/((1+t)^(2))dt in terms of a