Find the integration of the

Q: Use Integration by Substitution to find sin(x²) 2x dx Use Integration by Substitution to find cos(x)…

A: We have to find

Q: Using appropriate trigonometric substitution and changing the limit of integration, the integral…

A:

Q: Use integration by parts to show that for n > 2: / sin" x dx: 1 sin- x cos x + /sin-2 x dx.

A: To evaluate: ∫sinnx dx

Q: 1. S sin x cos 3x dx.

A:

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

A: To find the integrations.

Q: Evaluate the definite integral. sin x dx -dx J12 I+cos² x

A:

Q: Evaluate the integral / 8 cos (x) sin(2x) dx Note: Use an upper-case "C" for the constant of…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 9 cos X dx 3 + sin x

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) ∫(sin…

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Q: Use integration by parts to establish the reduction formula: Jx" cos x dx = x" sin x – n x"-1 sin x…

A:

Q: Evaluate the definite integral. 1. S(sin(2x) – cos(2x)) dx

A:

Q: Use the formula sin (x) dæ sin(2x) + C 4 and the reduction formula 1 -cos(x) sin"-'(x)+ n – 1 n-2…

A: the given integral,∫sin4(x)dx

Q: Evaluate the integral 3 4 sin° (x) cos (x) dx Note: Use an upper-case "C" for the constant of…

A: Give query is to eveluate the integral.

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

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) tan-(5x) dx 1 + 25x2 1 2…

A:

Q: (2) Compute the value |* sin(2r)dr and show the computations involved. If you are using substitu-…

A: We use integration by parts.

Q: Find the indefinite integral. ∫(x2 cos x)dx

A: The given integral is ∫x2cosx  dx. Let u=x2  and   dv=cosx dx. This implies that du=2xdx  and…

Q: C for the constant of integration.) Evaluate the definite integral. (Use sin(23x) xp 1 + cos (23x)…

A: The given integral is,

Q: Find the integral of the following equation integrate (cos x)/(1 - cos^2 x) dx

A:

Q: Find the indefinite integral.

A: Given,∫2sinxcosxdxwe need to find the indefinite integral

Q: Find the indefinite integral

A: To find the indefinite integral: ∫sinx7+cos2x dx Solution: Let substitute t=cosx Differentiating…

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

A:

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

A: Given :           ∫ sin9 xcos5 xdx

Q: Make a substitution to express the integrand as a rational function and then evaluate the integral 9…

A:

Q: Evaluate the integral. ∫ Cos2 x Sin2x dx

A: Given :           ∫cos2x sin2x dx

Q: Find the indefinite integral S (8x2/3 + 5* – cos(x))dx and verify the result by differentiation.

A:

Q: Select the basic integration formula you can use to find the indefinite integral. (6cos(20x))e…

A: Please refer the attached image for complete solution.

Q: evaluate using Integration by Parts, substitution, or both if necessary.

A: Given integral is By using the following substitution, we get

Q: Evaluate the integral sin x dx (2 + 3 cos x)2

A:

Q: S sin(4x +3)cos(3x – 5)dx -

A:

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

A:

Q: Find the indefinite integral ∫ 2sin x cos x dx

A: The given integral is ∫2sin(x)cos(x)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: 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: 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: Use integration by substitution and the Fundamental Theorem to evaluate the definite integral. 2 |…

A: Use substitution method

Q: Evaluate the definite integral. 1 2 sin-'(x) dx /1 – x²

A:

Q: Use an appropriate u-substitution to evaluate the indefinite integral 3sin (71)cos(7)dt. Use C'for…

A: Use substitutions to integration

Q: what is the integration of x^2/(9-x^2)^3/2 using trigonometric substitution

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Q: 03 cos(02) dO /2

A:

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

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Q: f sin-¹(x) dx

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Q: x³ cos4xdx (you can use short cut method)

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

A: Given: I=∫0π2sin x1+cos xdx

Q: sin34xdx Cos4x

A: Solving the problem by doing the integration of the given problem

Q: Use integration by parts to evaluate the integral: sin( – 8r)dr - 05 e-r(sin(-8r) - 8 cos (-8r)) + C

A:

Q: Use U-Substitution to evaluate the definite integrals. Sž cos 2x dx (1+x2)2

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Q: 1. Find the numerical Integration of cos(x) + sin(x) where n = 4 using trapezoidal rule.

A:

Q: Evaluate the definite integral. 1. 2 cos-¹(x) √1-x² dx

A: Given Problem:- ∫-11-2cos-1x1-x2dx

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.