6. Definite Integrals

What is the main difference between definite and indefinite integrals?

• Definite integrals are always positive, while indefinite integrals can be negative.

• Indefinite integrals have bounds, while definite integrals do not.

• Indefinite integrals are always positive, while definite integrals can be negative.

• Definite integrals have bounds, while indefinite integrals do not.

What is the integral of x^2 from 0 to 10?

• 500

• 333

• 1000/3

• 100

What does the process of evaluating a definite integral involve?

• Adding the initial and final bounds.

• Subtracting the initial bound from the final bound after plugging them into the integral.

• Dividing the initial bound by the final bound.

• Multiplying the initial and final bounds.

For the function y = x^2 - 5, what is the y-intercept?

• -5

• 10

• 5

• 0

For the function y = x^2 - 5, what are the x-intercepts?

• ±2

• ±3

• ±5

• ±√5

How can the integral of x^2 - 5 from -2 to 2 be simplified?

• By adding the integrals of x^2 and -5.

• By dividing the integral of x^2 by the integral of -5.

• By subtracting the integral of -5 from the integral of x^2.

• By multiplying the integrals of x^2 and -5.

What is the integral of x^2 from -2 to 2?

• 2/3

• 16/3

• 8/3

• 4/3

What is the integral of -5 from -2 to 2?

• -10

• 20

• -20

• 10

What is the final result of the integral of x^2 - 5 from -2 to 2?

• -16/3

• 8/3

• 16/3

• -8/3

Why might the area under the curve for y = x^2 - 5 from -2 to 2 be negative?

• Because the bounds are negative.

• Because the curve is below the x-axis.

• Because the curve is above the x-axis.

• Because the integral is always negative.