Understanding Integrals and Symmetry

What is the antiderivative of 9 - x^2?

• 9x - x^3/3

• 9x + x^3/3

• 9x + x^2/2

• 9x - x^2/2

What is the result of the integral of 9 - x^2 from 0 to 3?

• 9

• 18

• 27

• 36

How can symmetry help in calculating the integral from -3 to 3 of an even function?

• By halving the integral from 0 to 3

• By doubling the integral from 0 to 3

• By calculating only the positive side

• By ignoring the negative side

What is the integral of an odd function from -a to a?

• Always positive

• Depends on the function

• Always negative

• Always zero

What is the integral of 4x - x^3 from 0 to 2?

• 2

• 4

• 6

• 8

What is the integral of cosine from -π/2 to π/2?

• 0

• 1

• 2

• π

What is the integral of cosine from 0 to π/2?

• 2

• 1

• 0

• π

How can symmetry simplify the calculation of the integral of sine from 0 to 5π/2?

• By ignoring the negative values

• By considering only the first quadrant

• By using the symmetry of the sine wave

• By calculating the integral from 0 to π

What is the integral of sine from 0 to 2π?

• 0

• 1

• 2

• π

What is the integral of sine from 0 to π/2?

• 2

• 1

• 0

• π