Evaluate \(\int_5^6 x(x-5)^{12} dx\).
A0.456
B0.556
C0.656
D0.756
Mathematics · Question Bank
Integral Calculus
10 of 67 questions match. Answer in your head first, then check the solution.
Evaluate \(\int_0^1 \frac{x dx}{(x+1)^8}\).
A0.011
B0.022
C0.033
D0.044
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\(\ln(e^x+1)^2-x+C\)
Evaluate \(\int_0^{\pi/2}\int_0^1\int_0^2 z dz r^2 dr \sin u du\).
A2/3
B4/3
C1/3
D5/3
Find the length of arc of the parabola \(x^2=4y\) from \(x=-2\) to \(x=2\).
A4.2 units
B4.6 units
C4.9 units
D5.2 units
Find the surface area (in square units) generated by rotating the parabola arc \(y=x^2\) about the x-axis from \(x=0\) to \(x=1\).
A5.33
B4.98
C5.73
D4.73
The area in the second quadrant of the circle \(x^2+y^2=36\) is revolved about the line \(y+10=0\). What is the volume generated?
A2218.33
B2228.83
C2233.43
D2208.53
Evaluate \(\displaystyle\iint 2r^2\sin\theta\cos^2\theta\,dr\,d\theta\) for \(0 \le r \le \sin\theta\), \(0 \le \theta \le \dfrac{\pi}{2}\).
A\(\dfrac{\pi}{2}\)
B\(\dfrac{\pi}{8}\)
C\(\dfrac{\pi}{24}\)
D\(\dfrac{\pi}{48}\)
Find the length of the arc of \(6xy = x^4 + 3\) from x = 1 to x = 2.
A1.34
B1.63
C1.42
D1.78
The area bounded by the curve \(y^2 = 12x\) and the line x = 3 is revolved about the line x = 3. What is the volume generated?
A186
B179
C181
D184