U-substitution with Indefinite & Definite Integrals - Practice "Find & Prove"

This is an engaging and self-checking practice on evaluating indefinite and definite integrals using u-substitution. Students are given 12 problems as each problem consists of two sub problems a) and b). In sub problem a) students have to find an indefinite integral and then in sub problem b) to prove that a definite integral having the same integrand as the integrand of the indefinite integral in a) is equal to a given number or а numerical expression. If students succeed in proving the equality involving the definite integral in b) problem, then they have succeeded in evaluating the indefinite integral in a). I hope the given equalities that students have to prove stimulate them to complete the both tasks of each problem.

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