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
15 of 67 questions match. Answer in your head first, then check the solution.
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 \(\sin^5 x dx\) if the lower limit is 0 and the upper limit is \(\pi/2\)?
A0.233
B0.333
C0.433
D0.533
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 the integral of \(\cos x dx\) limits from \(\frac{\pi}{4}\) to \(\frac{\pi}{2}\)
A0.423
B0.293
C0.923
D0.329
The integral of \(\cos x\) with respect to x is
A\(\sin x+C\)
B\(\sec x+C\)
C\(-\sin x+C\)
D\(\csc x+C\)
What is the area (in square units) bounded by the curve \(y^2=x\) and the line \(x-4=0\)?
A30/3
B31/3
C32/3
D29/3
Find the area bounded by the parabola \(x^2=4y\) and \(y=4\).
A21.33
B33.21
C31.32
D13.23
What is the area bounded by the curve \(y=x^3\), the x-axis and the line \(x=-2\) and \(x = 1\)?
A4.25
B2.45
C5.24
D5.42
Find the area in the first quadrant bounded by the parabola \(y^2=4x\), \(x=1\) & \(x=3\)
A9.555
B9.955
C5.955
D5.595
What is the area between \(y=0\), \(y=3x^2\) \(x=0\) and \(x=2\)?
A8
B24
C12
D6
What is the area bounded by the curve \(y^2=x\) and the line \(x-4=0\)?
A11
B31/3
C10
D32/3
Find the centroid of the upper half of the circle \(x^2 + y^2 = 9\).
A(0, 3/π)
B(0, 4/π)
C(0, 5/π)
D(0, 6/π)
If \(f'(x) = \sin x\) and \(f(\pi) = 3\), then \(f(x) =\)
A4 + cos x
B3 + cos x
C2 − cos x
D4 − cos x
Find the area of the region between the x-axis and \(y = (x - 1)^2\) from x = 0 to x = 2.
A1/3
B2/3
C1/2
D1/4