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Quiz 1
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\(\int \frac{x+\sin x}{1+\cos x}\) dx is equal to
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log |1 + cos x | + c
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log | x + sin x | + c
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x – tan + c
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x. tan \(\frac{x}{2}\) + c
Explanation
x. tan \(\frac{x}{2}\) + c
∫1.dx =
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x + k
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1 + k
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\(\frac{x^2}{2}\) + k
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log x + k
Explanation
x + k
∫\(\frac{dx}{√x}\) =
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√x + k
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2√x + k
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x + k
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\(\frac{2}{3}\)x + k
Explanation
2√x + k
∫\(\frac{dx}{1+cos x}\) =
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tan \(\frac{x}{2}\) + k
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\(\frac{1}{2}\) tan \(\frac{x}{2}\) + k
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2 tan \(\frac{x}{2}\) + k
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tan² \(\frac{x}{2}\) + k
Explanation
tan \(\frac{x}{2}\) + k
\(\int_{a}^{b}\) x dx =
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tan \(\frac{x}{2}\) + k
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\(\frac{1}{2}\) tan \(\frac{x}{2}\) + k
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2 tan \(\frac{x}{2}\) + k
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tan² \(\frac{x}{2}\) + k
Explanation
tan \(\frac{x}{2}\) + k
If x > a, ∫\(\frac{dx}{x^2-a^2}\) =
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\(\frac{2}{2a}\) log \(\frac{x-a}{x+a}\) + k
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\(\frac{2}{2a}\) log \(\frac{x+a}{x-a}\) + k
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\(\frac{1}{a}\) log(x² – a²) + k
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log(x + \(\sqrt{x^2-a^2}\) + k)
Explanation
\(\frac{2}{2a}\) log \(\frac{x-a}{x+a}\) + k
∫\(\frac{cos 2x dx}{(sinx+cosx)^2}\) =
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–\(\frac{1}{sinx+cosx}\) + c
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log | sin x + cos x | + c
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log | sin x – cos x | + c
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\(\frac{1}{(sinx+cosx)^2}\)
Explanation
log | sin x + cos x | + c
∫\(\frac{(1+logx)^2}{1+x^2}\) dx =
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\(\frac{1}{3}\)(1+log)³ + c
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\(\frac{1}{2}\)(1+log)² + c
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log (log 1 + x) + 2
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None of these
Explanation
\(\frac{1}{3}\)(1+log)³ + c
\(\int_{0}^{1}\frac{(tan^{-1}x)^2}{1+x^2}\) dx =
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1
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\(\frac{π^2}{64}\)
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\(\frac{π^2}{192}\)
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None of these
Explanation
\(\frac{π^2}{192}\)
\(\int_{-2}^{2}\) |x|dx =
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0
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2
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1
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4
Explanation
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∫\(\frac{x^4+1}{x^2+1}\) dx is equal to
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\(\frac{x^3}{3}\) + x + tan x + c
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\(\frac{x^3}{3}\) – x + tan x + c
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\(\frac{x^3}{3}\) + x + 2tan x + c
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\(\frac{x^3}{3}\) – x + 2tan x + c
Explanation
\(\frac{x^3}{3}\) – x + 2tan x + c
∫(√x + \(\frac{1}{√x}\)) dx =
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\(\frac{1}{x}\) x+ 2x+ c
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\(\frac{2}{3}\) x+ \(\frac{1}{2}\)x+ c
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\(\frac{2}{3}\) x+ 2x+ c
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\(\frac{3}{2}\) x+ \(\frac{1}{2}\)x+ c
Explanation
\(\frac{2}{3}\) x+ 2x+ c
∫\(\frac{sin^2x-cos^2x}{sin^2xcos^2x}\) dx is equal to
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tan x + cos x + c
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tan x + cosec x + c
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tan x + cot x + c
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tan x+ sec x + c
Explanation
tan x + cot x + c
\(\frac{d}{dx}\)∫f(x)dx is equal to
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f'(x)
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f(x)
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f'(x’)
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f(x) + c
Explanation
f(x)
What is the value of \(\int_{0}^{\pi / 2}\) \(\frac{\sqrt{tan x}}{\sqrt{tan x}+\sqrt{cot x}}\) dx?
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\(\frac{π}{2}\)
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\(\frac{π}{4}\)
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\(\frac{π}{8}\)
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None of these
Explanation
\(\frac{π}{4}\)
What is the value of \(\int_{0}^{\pi / 2}\) \(\frac{sinx – cos x}{1+sin xcos x}\) dx?
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1
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\(\frac{π}{2}\)
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0
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–\(\frac{π}{2}\)
Explanation
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What is the value of \(\int_{\pi / 6}^{\pi / 3}\) \(\frac{dx}{sin2x}\)?
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\(\frac{1}{2}\) log(-l)
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log(- 1)
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log 3
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log √3
Explanation
log 3
What is the value of \(\int_{-1}^{1}\) sin³ x cos² xdx?
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0
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1
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\(\frac{1}{2}\)
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2
Explanation
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What is the value of \(\int_{1}^{e} \frac{1+\log x}{x}\) dx?
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\(\frac{3}{2}\)
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\(\frac{1}{2}\)
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e
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\(\frac{1}{e}\)
Explanation
\(\frac{3}{2}\)
\(\int_{-\pi / 2}^{\pi / 2}\) sin xdx =
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-1
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0
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1
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None of these
Explanation
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