Which of the following methods is most efficient for evaluating the integral: in

Question

Which of the following methods is most efficient for evaluating the integral: integral sin^8 (x) cos (x) dx Select only ONE answer. u-substitution using half-angle formulas to re-write sin^8 x integration by parts If we want to evaluate integral Squareroot 36 - x^2 dx using a trigonometric substitution, which of the following is the best substitution to use? Select only ONE answer. x = 6 tan(theta) x = 6 sin(theta) x = 1/6 sin(theta) x = sin(theta) x = tan(theta) x = 1/6 sec(theta) x = sec(theta)

Explanation / Answer

1), We know that derivative of sin(x) is cos(x), therefore, we can easily substitute u=sin(x) to make the given integrals a simple power function. Therefore, u-substitution is most suitable.

2) The given integral can be easily evaulated by plugging either x=6cos(theta) or x=6sin(theta). Therefore, second option is correct.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.