Calculus: Integrals and Trigonometric Functions

The video tutorial explains how to integrate the function cosine x from 0 to Pi/2 using the fundamental theorem of calculus. It covers finding the antiderivative of cosine x, which is sine x, and evaluates the definite integral by applying the limits of integration. The tutorial also provides a graphical interpretation, showing that the integral represents the area under the curve of cosine x above the x-axis, which equals one square unit.

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

• 1

• Pi

• 0

• 2

According to the fundamental theorem of calculus, what is required for the integrand function?

• It must be differentiable

• It must be discontinuous

• It must be constant

• It must be continuous

What is the anti-derivative of cosine x?

• tangent x

• secant x

• cosine x

• sine x

What is the value of sine at Pi/2?

• Pi

• 1

• 0

• -1

What is the value of sine at 0?

• -1

• 1

• 0

• Pi

What does the definite integral of cosine x from 0 to Pi/2 represent?

• The length of the curve

• The volume of the solid

• The area under the curve

• The slope of the tangent line

Why is the integrand function cosine x non-negative over the interval from 0 to Pi/2?

• Because cosine x is always positive

• Because cosine x is always negative

• Because cosine x is zero

• Because cosine x is non-negative

What is the area under the curve of cosine x from 0 to Pi/2?

• Pi square units

• 0.5 square units

• 1 square unit

• 2 square units

How is the area under the curve of cosine x from 0 to Pi/2 visually represented?

• As a circle

• As a shaded region

• As a point

• As a line

What is the relationship between the definite integral and the area under the curve?

• The integral equals the area

• The integral is always larger

• The area is always larger

• They are unrelated