Area Under the Curve Worksheet (Integration)

Question 1: Find the area under the curve of the function \( f(x) = 2x \) from \( x = 1 \) to \( x = 3 \). \[ \int_1^3 2x \, dx \]

Question 2: Find the area under the curve of the function \( f(x) = x^2 \) from \( x = 0 \) to \( x = 2 \). \[ \int_0^2 x^2 \, dx \]

Question 3: Find the area under the curve of the function \( f(x) = 3x - 1 \) from \( x = 2 \) to \( x = 5 \). \[ \int_2^5 (3x - 1) \, dx \]

Question 4: Find the area under the curve of the function \( f(x) = x^3 \) from \( x = 0 \) to \( x = 1 \). \[ \int_0^1 x^3 \, dx \]

Question 5: Find the area under the curve of the function \( f(x) = 4x + 2 \) from \( x = 1 \) to \( x = 3 \). \[ \int_1^3 (4x + 2) \, dx \]

Question 6: Find the area under the curve of the function \( f(x) = 5 - x^2 \) from \( x = -1 \) to \( x = 2 \). \[ \int_{-1}^2 (5 - x^2) \, dx \]

Question 7: Find the area under the curve of the function \( f(x) = 2x + 1 \) from \( x = 0 \) to \( x = 4 \). \[ \int_0^4 (2x + 1) \, dx \]

Question 8: Find the area under the curve of the function \( f(x) = x^2 + 3x \) from \( x = 1 \) to \( x = 4 \). \[ \int_1^4 (x^2 + 3x) \, dx \]

Question 9: Find the area under the curve of the function \( f(x) = 2x^2 + 3x \) from \( x = 0 \) to \( x = 2 \). \[ \int_0^2 (2x^2 + 3x) \, dx \]

Question 10: Find the area under the curve of the function \( f(x) = 3x^2 - 2x + 1 \) from \( x = 1 \) to \( x = 3 \). \[ \int_1^3 (3x^2 - 2x + 1) \, dx \]