Calculus I · Unit 3A · exam

Unit 3A Practice Exam B

Take Unit 3A Practice Exam B, a comprehensive BetterGrades integral-calculus practice exam with a separately routed worked answer key.

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Review, practice, exams, and answer keys

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Take Unit 3A Practice Exam B, a comprehensive BetterGrades integral-calculus practice exam with a separately routed worked answer key.

Notice

A complete response carries setup, method, computation, bounds or constants, units, interpretation, and an independent verification.

Decide

Attempt the entire problem first, then use one answer at a time to locate the earliest reasoning decision that needs repair.

Avoid

Reading a key before modeling the problem or treating every mismatch as algebra when the first error was conceptual.

Answer key published

Finish first. Then check every answer.

The complete numbered key is online as its own easy-to-find route.

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Practice Exam B

Exercise

Evaluate

\int\left(3x^{-1/2}+4e^x-5\cos x\right)\,dx.

Exercise

Use four right-endpoint rectangles to estimate

\int_0^2x^2\,dx.

Exercise

Find the average value of $f(x)=x^2+1$ on $[0,3]$ .

Exercise

Differentiate

H(x)=\int_{x^2}^{2x+1}\sqrt{1+t^4}\,dt.

Exercise

Evaluate

\int\frac{x}{(1+x^2)^3}\,dx.

Exercise

Evaluate

\int x^2\ln x\,dx.

Exercise

Evaluate

\int\sin^3x\cos^2x\,dx.

Exercise

Evaluate

\int\frac{dx}{x^2+9}.

State the substitution or standard form you use.

Exercise

Use the trapezoidal rule with $n=4$ to estimate

\int_0^2x^3\,dx.

Exercise

Determine whether

\int_0^1x^{-2/3}\,dx

converges. If it converges, find its value.

Exercise

Explain why $+C$ belongs on an indefinite integral but not on a completed definite-integral evaluation.

Exercise

For each integral, name the best first method and justify the choice in one sentence:

\int x\ln x\,dx, \qquad \int\frac{2x}{x^2+7}\,dx, \qquad \int\frac{dx}{x^2-4}.

Source & rights

Original instruction with traceable references.

BetterGrades-original; no direct adaptation declared in the verified handoff.

Reference textbooks remain rights-separated and are not published as application assets. Any direct adaptation requires separate identification and attribution.

Practice Exam B

Exercise

Evaluate

\int\left(3x^{-1/2}+4e^x-5\cos x\right)\,dx.

Exercise

Use four right-endpoint rectangles to estimate

\int_0^2x^2\,dx.

Exercise

Find the average value of $f(x)=x^2+1$ on $[0,3]$ .

Exercise

Differentiate

H(x)=\int_{x^2}^{2x+1}\sqrt{1+t^4}\,dt.

Exercise

Evaluate

\int\frac{x}{(1+x^2)^3}\,dx.

Exercise

Evaluate

\int x^2\ln x\,dx.

Exercise

Evaluate

\int\sin^3x\cos^2x\,dx.

Exercise

Evaluate

\int\frac{dx}{x^2+9}.

State the substitution or standard form you use.

Exercise

Use the trapezoidal rule with $n=4$ to estimate

\int_0^2x^3\,dx.

Exercise

Determine whether

\int_0^1x^{-2/3}\,dx

converges. If it converges, find its value.

Exercise

Explain why $+C$ belongs on an indefinite integral but not on a completed definite-integral evaluation.

Exercise

For each integral, name the best first method and justify the choice in one sentence:

\int x\ln x\,dx, \qquad \int\frac{2x}{x^2+7}\,dx, \qquad \int\frac{dx}{x^2-4}.

Source & rights

Original instruction with traceable references.

BetterGrades-original; no direct adaptation declared in the verified handoff.

Reference textbooks remain rights-separated and are not published as application assets. Any direct adaptation requires separate identification and attribution.

Finish first. Then check every answer.

Practice Exam B

Related resources

Original instruction with traceable references.

Finish first. Then check every answer.

Practice Exam B

Related resources

Original instruction with traceable references.