Mathematics Tes...

\(\frac{1}{c}\displaystyle \int_{ac}^{bc}f\left(\frac{x}{c}\right)dx\) is equal to

\(\int_{0}^{\pi /3}\sqrt{1+\sin 2x}\, dx\)

What is \(\rm \int^\frac{\pi}{2}_0 e^{ln(cos x)} dx\) equal to?

What is the value of \(\displaystyle \int_{-\pi/2}^{\pi/2}|\sin x|\:dx?\)

Find the value of a + b if \(\rm \int_{0}^{1} \frac{dt}{t^{2}+25}=\frac{1}{5}(tan^{-1}{b}-tan^{-1}{a)}\)

If f(2a - x) = f(x) and \(\displaystyle\int^{a}_0f(x)dx= \lambda\) then  \(\displaystyle\int^{2a}_0f(x)dx\) is:

Suppose, \(I = \rm \frac{d}{dx} \int_{\sin x}^{\cos x} \frac{1}{t} dt\), Then which of the following is the correct value of this given definite integral?

Let f(x) and g(x) be twice differentiable functions on [0, 2] satisfying f’’(x) = g”(x), f’(1) = 4, g’(1) = 6, f(2) = 3 and g(2) = 9. Then what is f(x) – g(x) at x = 4 equal to?

What is value of \(\rm \int_{-\pi/2}^{\pi/2} x^{5}\sin^{4}x dx\) ?

If f(x) = 2^x, then what is \(\int^{10}_2\frac{f'(x)}{f(x)}dx\) equal to?