What is the correct first step for the integral of sin cubed x dx?

• Split off one sin x and write the rest with sin squared = 1 minus cos squared
• Split off one cos x and substitute u = sin x at once
• Apply the half angle formula to sin cubed directly
• Write sin cubed as sin x times cos squared x

What is the correct first step for the integral of sin^3 x dx?

• Split off one sin x factor
• Apply a half-angle formula at once
• Set u = sin^3 x

An integrand contains sqrt(16 - x^2). In x = a sin theta, what is a?

• 2
• 16
• 4

After splitting sin^3 x, which identity converts what is left?

• sin^2 x = 1 + cos^2 x
• sin^2 x = 1 - cos^2 x
• sin^2 x = 2 cos^2 x

What is the correct first step for the integral of cos to the fifth x dx?

• Split off one cos x and write the rest with cos squared = 1 minus sin squared
• Split off one sin x and write everything in cosine
• Apply the half angle formula four times in a row
• Write cos to the fifth as cos x times tan to the fourth

Use x = sin theta to evaluate the integral from 0 to 1 of x/sqrt(1 - x^2) dx.

Which substitution fits an integrand with sqrt(x^2 + 4)?

• x = 2 sin theta
• x = 2 tan theta
• x = 2 sec theta

Which substitution fits an integrand containing sqrt of x squared plus 4?

• x = 2 tan theta
• x = 2 sin theta
• x = 4 tan theta
• x = 2 sec theta

With x = 2 sin theta you finish with an expression in theta. How do you return to x?

• Draw a right triangle and read off the sides
• Replace theta with x directly
• Differentiate the theta answer

With x = 2 sin theta you finish integrating and hold an expression in theta. How do you return to x?

• Draw a right triangle with sin theta = x over 2 and read off the other sides
• Replace every theta with x divided by 2
• Differentiate the theta expression with respect to x
• Set theta to arcsin x and leave it in inverse form