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Solve the following.
Show that .
Show that $\int_5^1 f(x) dx = -4$.
Answer
Answer
AIGiven $\int_1^5 3f(x) dx = 12 \Rightarrow 3\int_1^5 f(x) dx = 12 \Rightarrow \int_1^5 f(x) dx = 4$.
Using the property $\int_a^b f(x) dx = -\int_b^a f(x) dx$:
$\int_5^1 f(x) dx = -\int_1^5 f(x) dx = -4$. Hence proved.
From ISC 2027 Specimen Mathematics Paper 1, question 14(i).