Evaluate the integral of \(\frac{dx}{x+2}\) from \(-6\) to \(-10\).
A\(2^{1/2}\)
B\(1/2\)
C\(\ln 3\)
D\(\ln 2\)
Mathematics · Question Bank
Integral Calculus
42 of 67 questions match · page 1 of 3. Answer in your head first, then check the solution.
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\(\sin(2x^2+7)+C\)
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
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 \(\int_0^{\pi/6} (\cos 3A)^8 dA\).
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 \(\ln x dx\), 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\(e^{\sin 2x}+C\)
Evaluate the double integral of \(r \sin u dr du\), the limits of r is 0 and \(\cos u\) and the limits of u are 0 and pi.
A1
B1/2
C0
D1/3
Evaluate the integral of \((3x^2+9y^2) dx dy\) if the interior limits has an upper limit of y and a lower limit of 0, and whose outer limit has an upper limit of 2 and lower limit of 0.
A10
B20
C30
D40
Find the area of the region bounded by \(y^2=8x\) and \(y=2x\).
A1.22 sq. units
B1.33 sq. units
C1.44 sq. units
D1.55 sq. units
What is the area bounded by the curve \(x^2=-9y\) and the line \(y+1=0\)?
A3 sq. units
B4 sq. units
C5 sq. units
D6 sq. units
Find the area bounded by the curve \(y=x^2+2\), and the lines \(x=0\) and \(y=0\) and \(x=4\).
A88/3
B64/3
C54/3
D64/5
Find the area bounded by the parabolas \(y=6x-x^2\) and \(y=x^2-2x\). Note: The parabolas intersect at points \((0,0)\) and \((4,8)\).
A44/3 square units
B64/3 square units
C74/3 square units
D54/3 square units
Find the area bounded by the line \(x-2y+10=0\), the x-axis, the y-axis and \(x=10\).
A75
B50
C100
D25
What is the area (in square units) bounded by the curve \(y^2=4x\) and \(x^2=4y\)?
A5.33
B6.67
C7.33
D8.67
Find the area enclosed by the curve \(x^2+8y+16=0\) the x-axis, the y-axis and the line \(x-4=0\).
A7.67 sq. units
B8.67 sq. units
C9.67 sq. units
D10.67 sq. units