Methods2025 Exam 2 Section A · Q17CAS active1 mark

Comparing definite integrals from graphs

Option A: an upward-opening parabola with a positive y-intercept, crossing the x-axis at x = 1 and x = 3, with its minimum just below the axis at x = 2.

Option B: a horizontal segment at a positive height ending in a closed dot at x = 2, then a steep straight line rising from an open circle below the x-axis at x = 2 and crossing the x-axis between 2 and 3.

Option C: a straight line through the origin rising to an open circle at x = 2, then a horizontal line at a lower positive height starting with a closed dot at x = 2 and continuing to the right.

Option D: a cubic-shaped curve through the origin that dips below the x-axis with a minimum near x = 0.8, crosses at x = 2, rises to a small maximum above the axis between 2 and 3, crosses again at x = 3 and then decreases steeply.

Given that $f : \R \to \R$ satisfies $\int_1^2 f(x)\,dx > \int_1^3 f(x)\,dx$ , the graph of $y = f(x)$ could be

1 mark

A(graph A)B(graph B)C(graph C)D(graph D)

Hints, answer checking and worked solutions come with a Season Pass.

Methods2025 Exam 2 Section A · Q17CAS active1 mark

Comparing definite integrals from graphs

Option A: an upward-opening parabola with a positive y-intercept, crossing the x-axis at x = 1 and x = 3, with its minimum just below the axis at x = 2.

Option C: a straight line through the origin rising to an open circle at x = 2, then a horizontal line at a lower positive height starting with a closed dot at x = 2 and continuing to the right.

Given that $f : \R \to \R$ satisfies $\int_1^2 f(x)\,dx > \int_1^3 f(x)\,dx$ , the graph of $y = f(x)$ could be

1 mark

A(graph A)B(graph B)C(graph C)D(graph D)

Hints, answer checking and worked solutions come with a Season Pass.