\(\int_{0}^{\pi^{2} / 4} \frac{\sin \sqrt{y}}{\sqrt{y}}\)
  • 1
  • 2
  • \(\frac{π}{4}\)
  • \(\frac{π^2}{8}\)
\(\int_{0}^{\infty} \frac{1}{1+e^{x}}\) dx =
  • log 2
  • -log 2
  • log 2 – 1
  • log 4 – 1
\(\int_{0}^{1}\) x(1 – x) is equal to
  • \(\frac{1}{10010}\)
  • \(\frac{1}{10100}\)
  • \(\frac{1}{1010}\)
  • \(\frac{11}{10100}\)
What is the value of \(\int_{0}^{1}\) \(\frac{d}{dx}\){sin(\(\frac{2x}{1+x^2}\))}dx?
  • 0
  • π
  • -π
  • \(\frac{π}{2}\)
\(\int_{0}^{1}\) \(\frac{x}{1+x}\) dx =
  • 1 – log 2
  • 2
  • 1 + log 2
  • log 2
∫\(\frac{sin x + cos x}{\sqrt{1+2sin x}}\) dx =
  • log(sin x – cos x)
  • x
  • log x
  • log sin (cos x)
∫log xdx =
  • log 10.x log(\(\frac{x}{e}\)) + c
  • log e.x log(\(\frac{x}{e}\)) + c
  • (x – 1) log x + c
  • \(\frac{1}{x}\) + c
∫(\(\frac{cos 2θ – 1}{cos 2θ + 1}\)) dθ =
  • tan θ – θ + c
  • θ + tan θ + c
  • θ – tan θ + c
  • -θ – cot θ + c
∫\(\frac{2dx}{\sqrt{1-4x^2}}\) =
  • tan (2x) + c
  • cot (2x) + c
  • cos(2x) + c
  • sin(2x) + c
Value of ∫\(\frac{dx}{\sqrt{2x – x^2}}\)
  • sin(x – 1) + c
  • sin(1 + x) + c
  • sin(1 + x²) + c
  • –\(\sqrt{2x-x^2}\) + c
∫x² sin x³ dx =
  • \(\frac{1}{3}\) cos x³ + c
  • –\(\frac{1}{3}\) cos x + c
  • \(\frac{-1}{3}\) cos x³ + c
  • \(\frac{1}{2}\) sin² x³ + c
∫\(\frac{cos 2x- cos 2θ}{cos x – cos θ}\)dx is equal to
  • 2 (sin x + x cos θ) + C
  • 2 (sin x – x cos θ) + C
  • 2 (sin x + 2x cos θ) + C
  • 2 (sin x – 2x cos θ) + C
∫\(\frac{dx}{sin(x-a)sin(x-b)}\) is equal to
  • sin(b – a) log |\(\frac{sin (x-b)}{sin(x-a)}\)| + C
  • cosec (b – a) log |\(\frac{sin (x-b)}{sin(x-b)}\)| + C
  • cosec (b – a) log |\(\frac{sin (x-b)}{sin(x-a)}\)| + C
  • sin (b – a) log |\(\frac{sin (x-a)}{sin(x-b)}\)| + C
∫tan √xdx is equal to
  • (x + 1)tan √x – √x + C
  • x tan √x – √x + C
  • √x – x tan √x + C
  • √x – (x + 1)tan √x + C
∫e(\(\frac{1-x}{1+x^2}\))² dx is equal to
  • \(\frac{e^x}{1+x^2}\) + C
  • –\(\frac{-e^x}{1+x^2}\) + C
  • \(\frac{e^x}{(1+x^2)^2}\) + C
  • \(\frac{-e^x}{(1+x^2)^2}\) + C
If ∫\(\frac{dx}{(x+2)(x^2+1)}\) = a log |1 + x²| + b tan x + \(\frac{1}{5}\) log |x + 2| + C, then
  • a = \(\frac{-1}{10}\), b = \(\frac{-2}{5}\)
  • a = \(\frac{1}{10}\), b = \(\frac{-2}{5}\)
  • a = \(\frac{-1}{10}\), b = \(\frac{2}{5}\)
  • a = \(\frac{1}{10}\), b = \(\frac{2}{5}\)
∫ \(\frac{x^3}{x+1}\) is equal to
  • x + \(\frac{x^2}{2}\) + \(\frac{x^3}{3}\) – log |1 – x| + C
  • x + \(\frac{x^2}{2}\) – \(\frac{x^3}{3}\) – log |1 – x| + C
  • x + \(\frac{x^2}{2}\) – \(\frac{x^3}{3}\) – log |1 + x| + C
  • x + \(\frac{x^2}{2}\) + \(\frac{x^3}{3}\) – log |1 + x| + C
If ∫\(\frac{x^3dx}{\sqrt{1+x^2}}\) = a(1 + x²)+ b\(\sqrt{1 + x^2}\) + C, then
  • a = \(\frac{1}{3}\), b = 1
  • a = \(\frac{-1}{3}\), b = 1
  • a = \(\frac{-1}{3}\), b = -1
  • a = \(\frac{1}{3}\), b = -1
\(\int_{-\pi / 4}^{\pi / 4}\) \(\frac{dx}{1+cos 2x}\) dx is equal to
  • 1
  • 2
  • 3
  • 4
\(\int_{0}^{\pi / 2}\) \(\sqrt{1+sin 2x}\) dx is equal to
  • 2√2
  • 2(√2 + 1)
  • 0
  • 2(√2 – 1)
0 h : 0 m : 1 s

Answered Not Answered Not Visited Correct : 0 Incorrect : 0