Challenging Maths (CALCULUS)

Day - 1

1) 

2) If y= {sin(x/2) + cos (x/2)}² then find the value of d³⁾²y/dx³⁾².

3) Prove 

4) ∫ dx/(1+ Sinx + cosx) 

5) Show: 0 < ¹₀ ∫ {x⁴(1- x)⁴/(1+ x²) = 22/7 - π

6) ∫ x dx/cos²x at (π/4,0) is


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