Antidifferentiation — Quiz 1
Practice Antidifferentiation — Quiz 1 on The School of Mathematics (Antidifferentiation) with 10 scored questions. This set covers problems such as: “\int\left(x-\frac{1}{x}\right)^2dx= ?”; “\int\frac{2-4y}{\sqrt{3y-2y^2}}dy= ?”; “\int\frac{y\,dy}{\sqrt{9-y^2}}= ?”. Work carefully, check explanations for misses, then retake to track improvement before test day.
Questions in this quiz (10)
$$\int(4x^2-3x+2)dx=$$?
- $$\frac{4}{3}x^3-\frac{3}{2}x^2+2x+C$$
- $$4x^3-3x^2+2x+C$$
- $$\frac{4}{3}x^3-\frac{3}{2}x^2+2+C$$
- $$\frac{1}{2}(4x^2-3x+2)^2+C$$
$$\int\left(x-\frac{1}{x}\right)^2dx=$$?
- $$\frac{x^3}{3}-2x+\frac{1}{x}+C$$
- $$\frac{x^3}{3}-2x-\frac{1}{x}+C$$
- $$\frac{x^3}{3}-2x+\frac{1}{x}+C$$
- $$\frac{x^3}{3}-x-\frac{1}{x}+C$$
$$\int\sqrt{5-3t}dt=$$?
- $$\frac{2}{9}(5-3t)^{3/2}+C$$
- $$-\frac{1}{3}(5-3t)^{3/2}+C$$
- $$\frac{4}{9}(5-3t)^{3/2}+C$$
- $$-\frac{2}{9}(5-3t)^{3/2}+C$$
$$\int\frac{2-4y}{\sqrt{3y-2y^2}}dy=$$?
- $$\sqrt{3y-2y^2}+C$$
- $$2\sqrt{3y-2y^2}+C$$
- $$\frac{1}{2}\sqrt{3y-2y^2}+C$$
- $$4\sqrt{3y-2y^2}+C$$
$$\int\frac{5du}{2+5u}=$$?
- $$5\ln|2+5u|+C$$
- $$\frac{1}{5}\ln|2+5u|+C$$
- $$\frac{5}{2+5u}+C$$
- $$\ln|2+5u|+C$$
$$\int\sin(4x)dx=$$?
- $$-\cos(4x)+C$$
- $$-\frac{1}{4}\cos(4x)+C$$
- $$\frac{1}{4}\cos(4x)+C$$
- $$4\cos(4x)+C$$
$$\int\frac{y\,dy}{\sqrt{9-y^2}}=$$?
- $$\frac{1}{3}\sin^{-1}\frac{1}{3}y+C$$
- $$-\sqrt{9-y^2}+C$$
- $$\sin^{-1}\frac{1}{3}y+C$$D. $$\sqrt{9-y^2}+C$$
- $$\sqrt{9-y^2}+C$$
$$\int\frac{dx}{1+9x^2}=$$?
- $$\tan^{-1}(3x)+C$$
- $$\frac{1}{3}\tan^{-1}(3x)+C$$
- $$\frac{1}{9}\ln(1+9x^2)+C$$
- $$\frac{1}{3}\ln|1+9x^2|+C$$
$$\int\left(\sqrt{t}-\frac{2}{\sqrt{t}}\right)^2dt=$$?
- $$\frac{t^2}{2}-4t+4\ln|t|+C$$
- $$\frac{t^2}{2}-2t+2\ln|t|+C$$
- $$\frac{t^2}{2}-4t+4\ln|t|+C$$
- $$t^2-4t+4\ln|t|+C$$
$$\int\left(6x^{1/2}-4x^{3/2}-x^{-1/2}\right)dx=$$?
- $$4x^{3/2}-\frac{8}{5}x^{5/2}-2x^{1/2}+C$$
- $$4x^{3/2}-\frac{8}{5}x^{5/2}+2x^{1/2}+C$$
- $$3x^{3/2}-\frac{4}{5}x^{5/2}-2x^{1/2}+C$$
- $$6x^{3/2}-\frac{8}{9}x^{5/2}-x^{1/2}+C$$
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Frequently asked questions
How many questions are in Antidifferentiation — Quiz 1?
This practice set includes 10 questions. Finish in one sitting when possible, then review incorrect answers before retaking.
What topic does Antidifferentiation — Quiz 1 cover?
Antidifferentiation — Quiz 1 focuses on Antidifferentiation. Questions follow exam-style wording and difficulty so you can practice the skills tested on major Antidifferentiation assessments. These are practice materials, not official exam questions.
How is Antidifferentiation — Quiz 1 scored?
Your score is the percentage of correct answers. A typical passing score is 80%. After you finish, review each miss with the available explanations on The School of Mathematics.
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