Solve l=int(cos^(4)t)^(-sin^(4)t)(sqrt(...

Solve `l=int_(cos^(4)t)^(-sin^(4)t)(sqrt(f(z))dz)/(sqrt(f(cos 2 t -z))+sqrt(f(z)))`

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int(dz)/(z sqrt(z^(2)-1))

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If x=int_(0)^(t^(2))e^(sqrt(z)){(2tan sqrt(z)+1-tan^(2)sqrt(z))/(2sqrt(z)sec^(2)sqrt(z))}dz and y=int_(0)^(t^(2))e^(sqrt(z)){(1-tan^(2)sqrt(z)-2tan sqrt(z))/(2sqrt(z)sec^(2)sqrt(z))}dz : Then the inclination of the tangent to the curve at t=(pi)/(4) is :

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If int_(x^(2))^(x^(4)) sin sqrt(t) dt, f'(x) equals

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Prove that: y=int_(1/8)^(sin^2x)sin^(-1)sqrt(t)dt+int_(1/8)^(cos^2x)cos^(-1)sqrt(t) , where 0lt=xlt=pi/2 , is the equation of a straight line parallel to the x-axis. Find the equation.

(i) If f(x) = int_(0)^(sin^(2)x)sin^(-1)sqrt(t)dt+int_(0)^(cos^(2)x)cos^(-1)sqrt(t) dt, then prove that f'(x) = 0 AA x in R . (ii) Find the value of x for which function f(x) = int_(-1)^(x) t(e^(t)-1)(t-1)(t-2)^(3)(t-3)^(5)dt has a local minimum.

Statement-1: int_(0)^(sin^(2)x) sin^(-1)sqrt(t )dt+int_(0)^(cos^(2)x) cos^(-1)sqrt(t )dt=(pi)/(4) for all x. Statement-2: (d)/(dx) int_(theta(x))overset(psi(x)) f(t)dt=psi'(x)f(psi(x))-theta'(x)f(theta(x))

ARIHANT MATHS ENGLISH-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)

Solve l=int(cos^(4)t)^(-sin^(4)t)(sqrt(f(z))dz)/(sqrt(f(cos 2 t -z))+...
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