Integrating for Area: 9th Grade Word Problems

A farmer wants to find the area of a rectangular field that is 50 meters long and 30 meters wide. Use integration to calculate the area.

• 1500 square meters

• 1800 square meters

• 1000 square meters

• 1200 square meters

A car travels along a straight road, and its speed is given by the function v(t) = 4t + 2, where t is in hours. Find the total distance traveled by the car from t = 1 to t = 3 hours using definite integrals.

• 20 miles

• 10 miles

• 15 miles

• 25 miles

A swimming pool is shaped like a rectangle with a length of 20 meters and a width of 10 meters. Calculate the area of the pool using integration.

• 150 square meters

• 250 square meters

• 100 square meters

• 200 square meters

The height of a hill can be modeled by the function h(x) = 3x^2 + 2, where x is the distance in meters from the base of the hill. Find the area under the curve from x = 0 to x = 4 meters.

• 80

• 72

• 64

• 56

A company produces a product, and the cost function is given by C(x) = 5x^2 + 3x + 10, where x is the number of units produced. Calculate the total cost of producing 1 to 5 units using definite integrals.

• 500.50

• 350.00

• 408.33

• 420.75

A water tank has a cross-sectional area given by A(h) = 2h + 1, where h is the height of the water in meters. Find the volume of water in the tank when the height is between 0 and 3 meters using integration.

• 8 cubic meters

• 5 cubic meters

• 12 cubic meters

• 15 cubic meters

The temperature of a substance is modeled by the function T(t) = 20 + 5sin(t), where t is in hours. Calculate the average temperature from t = 0 to t = 6 hours using definite integrals.

• 21.0

• 20.5

• 19.5

• 22.5

A park is designed in the shape of a semicircle with a radius of 10 meters. Calculate the area of the park using integration.

• 314.16 square meters

• 78.54 square meters

• 100 square meters

• 157.08 square meters

The revenue generated by a small business is modeled by the function R(x) = 10x - x^2, where x is the number of items sold. Find the total revenue from selling 1 to 4 items using definite integrals.

• 54

• 72

• 45

• 30

A cyclist rides along a path where the distance covered is given by the function d(t) = 2t^2 + 3t, where t is in hours. Calculate the total distance covered from t = 0 to t = 2 hours using integration.

• 11.33

• 9.75

• 10.00

• 12.50