(a) Express () n lim > sin - n i=1 as a definite integral.

Q: Evaluate the definite integral.

A: We have to evaluate the integration ∫0π3sec32xtanxdx

Q: Find the indefinite integral (tan -1æ}? dx. 1+ x2

A:

Q: Evaluate the indefinite integral. Use C as the constant of integration. -3+ 6 cos 0 do 02 sin 0

A: To Find: ∫-3+6cosθθ-2sinθdθ

Q: Evaluate the indefinite integral. sin(-3x) dx +C.

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos' (0) sin(0) dO

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(In 12x) dx Cos In x +…

A:

Q: ind the indefinite integral using the formulas from Theorem 5.25. (Use C for the constant of in 5 dx…

A:

Q: Evaluate the integral. ∫Sin-1 x dx

A:

Q: Evaluate the definite integral.

A:

Q: Q2 : Evaluate the integral sin x dx 1-sin² x

A: To find the integrations.

Q: 1 * dx 1+ sin x + cos x

A:

Q: Evaluate the integral [ ª sin(tan x) dx cos² x

A: Given- ∫sintanxcos2xdx To find- The value of the above integral. Concept Used- The above integral…

Q: Evaluate the indefinite integral. [ (sin-æ)3 dx : +C. V1 - x2

A:

Q: Evaluate the indefinite integral; f cos x sin x dx

A:

Q: f. f S tan° r sec xdr tanx sec

A:

Q: cos xdx sin x

A:

Q: Evaluate the indefinite integral. | = sin(x) cos(4x) dx +C

A: Given query is to find the intersection.

Q: Evaluate the definite integral. Use a graphing utility to verify your result.

A:

Q: Evaluate the definite integral. sec (x) tan (x) dx =

A:

Q: Evaluate the indefinite integral: ∫ x2 sin(x3 + 1) dx

A: ∫x2sinx3+1dx

Q: Evaluate the indefinite integral.   ∫x2 Cos( x3) dx

A:

Q: Evaluate the definite integral. ec (x) tan (x) dx : sec 0.

A: ∫secxtanx=secx

Q: Evaluate the indefinite integral: tan(0) cos(0) c

A: Given: ∫tan2θcosθdθ

Q: 5. Express lim 2 cos as a definite integral, then find t

A:

Q: 7. Find the integral of the hyperbolic function below. 6 sin(x) cosh[cos(x)] dx

A: Evaluate: ∫6 sinx coshcosx dx

Q: Evaluate the indefinite integral.

A: Consider the given integral I=∫sec3x·tanx dx

Q: Evaluate the indefinite integral -3 tan (x) sec'(x) dx +C

A: Given,

Q: Find the indefinite integral. x +8 -dx X +8 -dx (Use C as the arbitrary constant.)

A: Given,

Q: Find the indefinite integral. ∫cos5 x sin x dx

A: ∫cos5x sinx dx Put, cosx=t⇒-sinx=dtdx⇒-sinx dx=dt⇒sinx dx=-dt

Q: (ii) Hence, by using Leibniz Rule for Differentiation Under the Integral Sign, compute the value of…

A: Leibniz Rule for Differentiation under integral sign:- ∂∂t∫atbtfx, tdx=∫atbt∂f∂tdx   + fbt, t∂bt∂t-…

Q: B. Evaluate the definite integral using the Simpson's rule, giving the answer correct to 3 decimal…

A:

Q: (a) Evaluate the indefinite integral (anti-derivative) x°(1+ 2*)® dx by using the substitution u =…

A:

Q: (a) Integrate the following definite integrals by using suitable method: (i) S tan-1 x dx

A:

Q: (-4 sec Xtanx-7sec K,

A:

Q: Find the indefinite integral using any method ∫ sin   cos   d

A:

Q: .. a) Show that sinh(2x) sinh(x). = 2 sinh(x) cosh(x), using the exponential definitions for cosh(x)…

A: Hyperbolic functions are defined using exponential functions. The hyperbolic function sinhx is…

Q: Solve the definite integral ro e(arcsin(x)) dx. V1 - x2

A:

Q: Find the indefinite integral ∫ sin x/(1 + cos x)   dx

A:

Q: Find the definite integral of sin x -dx 0 1+cos x

A: Given: I=∫0π2sin x1+cos xdx

Q: Find the indefinite integral. tan“ X dx sec x

A:

Q: Find the general indefinite integral.

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos(x) sin 1 (x) xp

A: ∫cosxsin16x dx

Q: a) Evaluate the integrals using appropriate substitutions. Sine ii) S - de Cos20+1

A:

Q: Evaluate the integral. 2 sin -1 x dx

A:

Q: Compute the indefinite integral. 1 – sin? x -dx cos x

A: Recall the trigonometric identity: sin2A + cos2A = 1 Hence, 1 - sin2A = cos2A

Q: (sin-l x)² dx V1-x²

A:

Q: Evaluate the indefinite integral 1 sec (x) tan(x) dx +C

A: Given,

Q: b) Evaluate the integral: S (sin-1(x))²dx

A:

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

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