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Exam-style questions from the same notes. Reveal the library answer when ready.

Integration by Substitution

Mathematics · Class 12

A function assigns exactly one output to each input in its domain. Domain contains allowed inputs; range contains attained outputs.

For y=uv, y'=u'v+uv'; differentiating each factor separately and multiplying is wrong.

Acceleration is a=dv/dt=d^2s/dt^2 and does not by itself tell the direction of motion.

tan(theta)=

An antiderivative F satisfies F'=f; indefinite integrals require +C because constants differentiate to zero.

Set angle mode correctly, state units, and check a principal answer against geometry or range.