Integration of Sin^2 x

The video tutorial demonstrates the integration of sin^2 x. Initially, a u-substitution is considered but found unsuitable due to the absence of cosine x in the integrand. Instead, a power reducing formula is applied, transforming sin^2 x into a form involving cosine 2x. The integration is then split into two parts, requiring another u-substitution for cosine 2x. The final result is simplified using a double angle identity, offering an alternative expression for the antiderivative.

What is the initial substitution considered for integrating sin^2 x?

• u = cos x

• u = x^2

• u = tan x

• u = sin x

Tags

CCSS.HSF.TF.A.4

Why does the initial u-substitution fail for integrating sin^2 x?

• The integrand does not contain cos x

• The integrand contains cos x

• The integrand contains tan x

• The integrand does not contain sin x

Tags

CCSS.HSF.TF.A.4

What formula is used to rewrite sin^2 x for integration?

• Double angle formula

• Sum-to-product formula

• Power-reducing formula

• Product-to-sum formula

What is the new substitution used to integrate cos 2x?

• u = x

• u = cos x

• u = sin x

• u = 2x

What is the result of integrating 1 with respect to x?

• 1

• x

• 0

• 2x

What is the anti-derivative of sin u in terms of u?

• sin u

• cos u

• -sin u

• -cos u

Tags

CCSS.HSF.TF.C.9

What is the constant of integration added to the anti-derivative?

• D

• E

• C

• F

Tags

CCSS.HSF.TF.C.9

How can sin 2x be expressed using a double angle identity?

• sin^2 x - cos^2 x

• 1 - 2 sin^2 x

• 2 cos^2 x - 1

• 2 sin x cos x

What is the alternative expression for the anti-derivative using the double angle identity?

• 12x - 4 sin x cos x + C

• 12x - 2 sin x cos x + C

• 12x + 4 sin x cos x + C

• 12x + 2 sin x cos x + C

What factor can be factored out from the alternative expression of the anti-derivative?

• 1

• 1/2

• 1/3

• 1/4