(x) dx =x arcsin(x) + /1 – x² + C arc

Q: ((cos 2x – sin? 3x)dx

A:

Q: Find the indefinite integral sec* 7x dx.

A: To find the indefinite integral of ∫sec47xdx

Q: Evaluate the following 1, the integral from 0 to π/2 of Cosx/(1+sin^2 x) dx 2, the integral from…

A: 1). the integral from 0 to π/2 of Cosx/(1+sin^2 x) dx   = arctan(sin(x))    Answer: π/4

Q: show how to use integration byparts to find integration (arcsin x)^2 dx

A: Let I=Arcsin x2 This can also be written as: I=sin-1x2 Now if we want to integrate above function we…

Q: First make a substitution and then use integration by parts to evaluate the integral. (Use C for the…

A: Given integration is, ∫sin-1lnxxdx Let, lnx=t⇒1xdx=dt

Q: Evaluate the definite integral.

A:

Q: S(1 - In =) 1 dx x2

A:

Q: Verify the integration formulas ∫sech x dx = sin-1 (tanh x) + C

A: To verify: The integration formula, Formula used:

Q: Evaluate the integral. arctan dx 1

A: For evaluating the given integral, we will use the concepts of integral by parts and integration…

Q: Evaluate the integral. ∫0 π/2  Sin2 x Cos 2 x dx

A: Consider the given integral as Use the identity to solve the integral such that

Q: a) Estimate the length of this arc with the length of the line segment joining the endpoints of the…

A:

Q: Evaluate the integral.  integral sin 3  x cos 5x dx

A:

Q: find integral tan 3 x dx

A: To find the integral of tan2x first split tan into two part and the using property of sec and tan…

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: Evaluate the definite integral.

A: Given,

Q: evaluate using Integration by Parts.

A:

Q: Find the length of the arc of x2 + y2 = 64 from x = -1 to x = -3, in the second quadrant. (Solve…

A: We need to find arc length.

Q: 3) Find the equation of the curve whose arclength from the point (4, 1) to the point (9, -1) is…

A:

Q: S) - aresin 2. 2 arcsin 2. is constant for 0sxs 4.

A:

Q: 10. Prove by using integration by change in variable the ff. integral: dx du = arcsec x + C xVx2 - 1

A: To show∫dxxx2-1=sec-1x+C.

Q: Evaluate the integral. (Use C for the constant of integration.) (arctan(x))5 | x2 + 1 dx

A:

Q: Use integration by parts, together with the techniques of this section, to evaluate the integral.…

A: Given: Let, By the rule of integration by parts.

Q: Find the integration: J* 1+sin X 4 dX Cos 2X

A: Introduction: Suppose, fx is a continuous function on the interval a,b. There is another…

Q: Evaluate using integration by parts. 1)x2 In 6x dx

A: We are asked  to evaluate the integral

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral SIn(tan x)…

A:

Q: Find the indefinite integral. ∫arctan x dx

A:

Q: dx = arcsec x + C xVx2 – 1

A:

Q: 1-sin 2x dx 2 x-sin x

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: Evaluate the integral ( Use C for the constant integration) ∫ 11 tan4(x) sec6(x) dx

A: I=∫11tan4x×sec6x dx=11∫tan4x×sec4x×sec2x dx=11∫tan4x×1+tan2x2×sec2x dx                      ⋯⋯(1)

Q: Prove by using integration by change in variable the ff. integral: dx = arcsec x +C xVx² – 1

A: Our Aim is to prove the given integral given below by using change of integration.∫dxx(x2-1)dx -(i)

Q: Use Property 8 to estimate the value of the integral.

A:

Q: Use integration tables to find or evaluate the integral ∫ 1 / (1 + tan x) dx

A: Given as- I=∫11+tanx To evaluate- The above integral using integration table. Identity Used-…

Q: Evaluate the integral.   ∫0√3 arctan(1/x) dx

A: Given:∫03 tan-11x dx

Q: Use integration tables to find or evaluate the integral ∫ 1 / sin   x cos   x dx

A: We have to evaluate the integral: ∫1sin x cos xdx We know the identity: sin2x+cos2x=1 Substituting…

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

A:

Q: 4. Use Trigonometric substitution method to evaluate the integral: dx

A:

Q: Solve the integral. cos x dx J (1+ sin² x) arctan (sin x) 10.

A: To evaluate:                      ∫cos x(1+sin2 x)arctan(sin x)dx    ... (1)

Q: Calculate the integral (sec(x)+ tan(x))² dx.

A:

Q: Find the indefinite integral. ∫4 arccos x dx

A: To evaluate the integral: ∫4cos-1x dx Integration by parts states that: ddxuv=v·ddxu-∫ddxv∫udxdx…

Q: Find the trigonometric integral ∫sin x cos4 x dx

A: Consider the integrals: ∫sinx·cos4xdx…

Q: |1- x 2 arctan + arcsin(2x – 1) = Hint using f Odx = C

A:

Q: Evaluate the integral.

A: Let the given integral be y - y = ∫sin-1x2dx            ...............(1)Let,x = sinθ…

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: Solve the integral 1 4. arcsin x dx 0.

A: Consider the given integral ∫01arcsinxdx. Let u=arcsinx,      and     dv=1. That implies, du=11-x2,…

Q: Evaluate the integration dx sin(x)" with h=0.5 by using 3/8 Simpson Rule. Write your answer in 4…

A: The formula for the Simpson's rule is . Here, the represents the value of the function at the…

Q: Find the indefinite integral ∫ [arctan(x/2)] / (4 + x2) dx

A: ∫arctanx24+x2dx Now put, arctanx2=t⇒11+x22·12=dtdx⇒11+x24·12=dtdx⇒44+x2·12=dtdx⇒24+x2=dtdx⇒14+x2…

Q: Solve the definite integral e(arcsin(x)) dx. /1 – x²

A:

Q: sin 2x dx

A: Given the integral

Q: QUESTION 3 Use integration by parts to evaluate the integral. 12x In (2x)dx

A: value=?