What is the integral of \((3t-1)^3 dt\)?
A\(\frac{1}{12}(3t-1)^4+C\)
B\(\frac{1}{12}(3t-4)^4+C\)
C\(\frac{1}{4}(3t-1)^4+C\)
D\(\frac{1}{4}(3t-1)^3+C\)
Mathematics · Question Bank
Integral Calculus
50 questions · page 1 of 3. Answer in your head first, then check the solution.
Evaluate the integral of \(\frac{dx}{x+2}\) from \(-6\) to \(-10\).
A\(2^{1/2}\)
B\(1/2\)
C\(\ln 3\)
D\(\ln 2\)
Integrate \(x \cos(2x^2+7) dx\).
A\(\frac{1}{4}\sin(2x^2+7)+C\)
B\(\frac{1}{4}\cos(2x^2+7)+C\)
C\(\frac{(\sin \theta)}{4(x^2+7)}+C\)
D\(\sin(2x^2+7)+C\)
Integrate: \((7x^3+4x^2) dx\).
A\(\frac{7x^3}{3}+\frac{4x^2}{2}+C\)
B\(\frac{7x^4}{4}+\frac{4x^2}{5}+C\)
C\(\frac{7x^4}{4}+\frac{4x^3}{3}+C\)
D\(7x^4-\frac{4x}{2}+C\)
What is the integral of \(\sin^5 x \cos^3 x dx\) if the lower limit is zero and the upper limit is \(\pi/2\)?
A0.0203
B0.0307
C0.0417
D0.0543
What is the integral of \(\sin^5 x dx\) if the lower limit is 0 and the upper limit is \(\pi/2\)?
A0.233
B0.333
C0.433
D0.533
Find the integral of \(12 \sin^5 x \cos^5 x dx\) if lower limit \(= 0\) and upper limit \(= \pi/2\).
A0.2
B0.3
C0.4
D0.5
Evaluate the integral of \(\sin^6 x dx\) from 0 to \(\pi/2\).
A\(\frac{\pi}{32}\)
B\(\frac{2\pi}{17}\)
C\(\frac{3\pi}{32}\)
D\(\frac{5\pi}{32}\)
Evaluate \(\int_5^6 x(x-5)^{12} dx\).
A0.456
B0.556
C0.656
D0.756
Evaluate \(\int_0^1 \frac{x dx}{(x+1)^8}\).
A0.011
B0.022
C0.033
D0.044
Evaluate \(\int_0^{\pi/6} (\cos 3A)^8 dA\).
A\(\frac{27\pi}{363}\)
B\(\frac{35\pi}{768}\)
C\(\frac{23\pi}{765}\)
D\(\frac{12\pi}{81}\)
Integrate \(\frac{1}{3x+4}\) with respect to x and evaluate the result from \(x=0\) and \(x=2\).
A0.278
B0.336
C0.252
D0.305
Evaluate the integral \(\int \cos^2 y dy\)
A\(\frac{y}{2}+\frac{\sin 2y}{4}+C\)
B\(y+2\cos y+C\)
C\(\frac{y}{4}+\frac{\sin 2y}{4}+C\)
D\(y+\sin 2y+C\)
Integrate the square root of \((1-\cos x) dx\).
A\(-2\sqrt{2}\cos\frac{1}{2}x+C\)
B\(-2\sqrt{2}\cos x+C\)
C\(2\sqrt{2}\cos\frac{1}{2}x+C\)
D\(-2\sqrt{2}\cos x+C\)
Evaluate the integral of \(\cos x dx\) limits from \(\frac{\pi}{4}\) to \(\frac{\pi}{2}\)
A0.423
B0.293
C0.923
D0.329
Evaluate the integral of \(\ln x dx\), the limits are \(1\) and \(e\).
A0
B1
C2
D3
Evaluate \(\int_1^{10} \frac{2 \log_{10} e dx}{x}\)
A2.0
B49.7
C3.0
D5.12
What is the integral of \(\cos 2x e^{\sin 2x} dx\)?
A\(\frac{e^{\sin 2x}}{2}+C\)
B\(-\frac{e^{\sin 2x}}{2}+C\)
C\(-e^{\sin 2x}+C\)
D\(e^{\sin 2x}+C\)
The integral of \(\cos x\) with respect to x is
A\(\sin x+C\)
B\(\sec x+C\)
C\(-\sin x+C\)
D\(\csc x+C\)
Find the integral of \([e^x-1]\) divided by \([e^x+1] dx\)
A\(\ln(e^x-1)^2+x+C\)
B\(\ln(e^x+1)-x+C\)
C\(\ln(e^x-1)+x+C\)
D\(\ln(e^x+1)^2-x+C\)