List of top Mathematics Questions

Prove: \(∫^1_{-1}x^{17}cos^{4}xdx\)
Prove: \(∫_0^1x.e^x\ dx=1\)
Prove: \(∫_1^3\frac {dx}{x^2(x+1)}=\frac 23+log\frac 23\)
Evaluate the definite integral: \(∫^4_1[|x-1|+|x-2|+|x-3|]dx\)
Evaluate the definite integral: \(∫^π_0\frac{xtanx}{secx+tanx}dx\)
Evaluate the definite integral: \(∫_0^{\frac{π}{2}}sin2x\,tan^{-1}(sinx)dx\)

Examine the following functions for continuity.
(A) f(x) = x-5 
(B) f(x) =\(\frac {1}{x-5}\), x≠5 
(C) f(x) = \(\frac {x^2-25}{x+5}\), x≠-5 
(D) f(x) = |x-5|

Check whether the relation R in R defined as R = {(a, b): a ≤ b3} is reflexive, symmetric or transitive

Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
R = {(a, b): b = a + 1} is reflexive, symmetric or transitive. 

Evaluate the definite integral: \(\int_{0}^{\frac{\pi}{4}}\frac{sinx+cosx}{9+16sin2x}dx\)
Evaluate the definite integral: \(\int_{0}^{1}\frac{dx}{\sqrt{1+x}-\sqrt{x}}\)
Evaluate the definite integral: \(\int^{\frac{\pi}{6}}_{\frac{\pi}{3}}\frac{sinx+cosx}{\sqrt{sin2x}}dx\)
Evaluate the definite integral: \(\int_{0}^{\frac{\pi}{2}}\frac{cos^{2}xdx}{cos^{2}x+4sin^{2}x}\)
Evaluate the definite integral: \(\int_{0}^{\frac{\pi}{4}}(\frac{sinxcosx}{cos^{4}x+sin^{4}x})dx\)
Evaluate the definite integral: \(\int_{\pi}^{\frac{\pi}{2}}e^{x}(\frac{1-sinx}{1-cosx})dx\)
Integrate the function: \(\frac{\sqrt{x^{2}+1}[log(x^{2}+1)-2logx]}{x^{4}}\)
Integrate the function: \(tan^{-1}\sqrt{\frac{1-x}{1+x}}\)
Integrate the function: \(\frac{x^{2}+x+1}{(x+1)^{2}(x+2)}\)
Integrate the function: \(\frac{2+sin2x}{1+cos2x}e^{x}\)
Integrate the function: \(\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}\)
Integrate the function: \(\frac{1}{\sqrt{sin^{3}xsin(x+α)}}\)
Integrate the function: \(ƒ'(ax+b)[ƒ(ax+b)]^n\)
Integrate the function: \(e^{3log\ x}(x^4+1)^{-1}\)
Integrate the function: \(cos^3 x\ e^{log\ sin\ x}\)
Integrate the function: \(\frac {1}{(x^2+1)(x^2+4)}\)