Prob 1\nIf f (x) =intigral\nupper limit is x power 2\nand lower limit is 1/x squareroot of sin( t)dt, then find the value of f (1).\nProb 2\nLet a = min x2 + 4x + 5, x ? R andb = lim??0 1-cos 2?/?squarethen find the value of\na-b\na+b .\nProb 3\nThe value of the Integral\nupper limit is p/2\nlower limit is -p/2(ax^3cos x + b sin x + c)dx, depends on how many parameters among (a , b , c).Prob 4\nFind the value of the Integral\nupper limit is p/2\nlower limit is -p/2root of ( cos x - cos^3 x)dx.\nProb 5\nLet f (x) =integralupper limit is x\nlower limit is 0\n( 2u+1/u^2-2u+2 )du then find the least value of f (x) in [-1,1].\nProb 6\nFind the values of a for which the function f (x) = cos x - sin x + ax + b is decreasing.\nProb 7\nFind the area bounded by the curves y=x|x| , x - axis , x = 1 & x = -1.\nProb 8\nFor x > 0 let f (x) =integralupper limit isxlower limit is 1\nln(t)/1+t,\nFind the function f (x) + f (1/x) and show that f (e) + f (1/e) = 1/2.\nProb 9\nIs the function f (x) = |x^2 - x| differentiable at x = 2. If yes find it’s derivative.\nProb 10\nCheck the monotonicity of f (x) =x/sinxin (0, p/2).

Pushkar Aditya , 10 Years ago

Grade 7