Consider the integral | cos* x sin'x dx , where k is a positive integer. Using the methods discussed in Section 8.3, we can use a trigonometric identity and a u-substitution to convert the given integral to which of the following? du

Q: Find the integral. er sin(5x)dx - IT

A: Known integral formula:

Q: Evaluate the indefinite integral 2 sin°(s) s cos sds

A:

Q: Evaluate the integrals ∫sin4 2x cos 2x dx

A: I=∫ Sin4 2x Cos 2x dxLet Sin 2x=t2 Cos 2x dx=dtCos 2x dx=dt2

Q: S sin x In(cosx) dx

A: To evaluate the integral: I=∫sin x(ln (cos x)) dx Substitute  cos x=t⇒-sin x dx=dt⇒sin x dx=-dt

Q: Evaluate the improper integral or show that it diverges. 16 tan-1 x dx 1+x² | 0.

A:

Q: Only one of these calculations is correct to evaluate the definite integral 4 | x? cosh(x) dx 0.…

A: Formula for Simpson's 1/3rd rule ∫baf(x) dx= h/3[(y0=+yn)+4(y1+y3+........+yn-1)…

Q: Evaluate the integral.  integral sin 9  x cos 3x dx

A:

Q: Evaluate the definite integral (if it exists) 1/3 -4 sin(x) dz cos² (1) If the integral does not…

A: Substitute cos(x)=t⇒-sin(x)dx=dt At x = 0, t = 1 At x=π3, t=12 The definite integral is: I=4∫112dtt2

Q: Evaluate the indefinite integral )cos*(s)ds

A: We will let Sin(s) = t Cos(s) ds = dt

Q: Evaluate the integral using the methods covered in the text so far:                    ∫ cos x5−2…

A: I=∫cosx5-2sinxdx Let us suppose -2sinx=t, then Differentiating to both the sides w.r.t x-…

Q: Find integral of sin^2 (x/2) dx with bounds of 0 to pi

A: Find the integral of sin^2 (x/2) dx with the bounds 0 to π.

Q: Use the Table of Integrals to evaluate the integral.  ∫ sin2x cos x ln(sin x) dx

A: We have to evaluate ∫sin2x cosxlnsinxdx Let substitute  t=sinx ⇒dtdx=cosxdt=cosx dx Substituting…

Q: Evaluate the integrals ∫sin 2x cos 3x dx

A: We have to evaluate ∫sin2xcos3xdx. We know that 22sinA cosB=sinA+B+sinA-B Therefore,…

Q: What is the integral of sin^5 x dx if the lower limit is O and the upper limit is T/2?

A: We have to find out

Q: 3 4. sin x cos xdx

A: These formulae are used while solving the question:

Q: Evaluate the integral. integral  cos 3x  sin 2x dx

A:

Q: Use a suitable substitution to find the indefinite integral S csc(sin 0) · cos(0)d0

A:

Q: 2 sin(x) cos(5x) cos(x) dx

A: To Integrate: ∫2sin(x) cos (5x) cos(x) dx

Q: Evaluate the integral 5x sin (x2) dx by using any methods.

A:

Q: Evaluate the integral sin'7 x cos x dx

A:

Q: Evaluate the integral.  integral sin 9  x cos 5x dx

A: Given :           ∫ sin9 xcos5 xdx

Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: Evaluate the integrals. ∫x sin x2 cos8 x2 dx

A: Given,         ∫xsinx2cos8x2dx

Q: Evaluate the integral (exact value). e3x sin(10x) dx = %3D

A:

Q: S sin(4x +3)cos(3x – 5)dx -

A:

Q: If we are asked to find the indefinite integral of cos® x sin' x, which identity can we use to…

A:

Q: (a) Evaluate the integral sin* 4x cos3 4x dx

A: a) Evaluate the integral                                 ∫0π8 sin4 4x cos3 4x dx  Let us substitute…

Q: Evaluate the definite integral. sin(3t)dt Preview kl3

A:

Q: Find the indefinite integral ∫ cos2 x sin4 x dx

A: Given: I=∫cos2xsin4xdx we know that ∫sinnxdx=n-1n∫sinn-2xdx-cosxsinn-1xn                   ..1

Q: Evaluate the integral.  integral sin 6  x cos 5x dx

A:

Q: TC 4. sin(2x) cos(2x) dx

A: To evaluate the definite integral

Q: Find the trigonometric integral ∫cos3( x − 1) dx

A: Find the trigonometric integral ∫cos3( x − 1) dx

Q: 2) sin9xcos10xdx 3) sin xcos xdx XCOS dx 4) S

A:

Q: Evaluate the integrals ∫sin3 x cos4 x dx

A:

Q: To evaluate the / sin-(x) + sin(x) cos2(x) -dx using basic formula of integration (without using…

A: We need to find values of f(x).

Q: Evaluate the definite integral 15 sin (3x) cos(3x) dx

A:

Q: evaluate the integral using the methods covered in the text so far.

A:

Q: Evaluate integral 0 to pie sin 2 x cos 4 x dx

A: To Evaluate the integral given below:-I=∫0πsin2(x)cos4(x)dx

Q: Evaluate the integral of sin(4x) cos(3x) dx

A: We have to use 2sinAcosB= sin(A+B)+sin(A-B) formula to simplify first.

Q: Find the trigonometric integral ∫sin2 x cos3 x dx

A: We have to find the trigonometric integral: ∫sin2 x cos3 x dx Rewriting the integral, ∫sin2 x cos3 x…

Q: Evaluate the integrals ∫cos3 2x sin5 2x dx

A: Evaluate: ∫cos32xsin52xdx

Q: Evaluate the integral.  integral sin 3  x cos 2 x dx

A:

Q: Use integration by parts to evaluate the integral: sin(-10r) dr e12r

A:

Q: Evaluate the integral (exact value). e2X sin(8x) dx = %3D

A: We can evaluate the given Integral by using the integration by parts method

Q: Suppose you calculated an integral using the trigonometric substitution x = 3sin(0), and got your…

A:

Q: cos ) ydydx sin

A:

Q: Evaluate the integral. 6 sin -1 x dx

A: Given problem:- ∫ 6sin-1(x) dx

Q: Find the indefinite integral  ∫sin3 x cos2 x dx

A: We have to find the indefinite integral ∫sin3 x cos2 x dx

Q: Evaluate integral 0 to pie sin 2 x cos 3 x dx

A: Explanation: Given that,  ∫0πsin2xcos3xdx   Formula Used: Trig. identity:1-sin2x=cos2xSum rule of…