프N4 + x2 dx 2

Q: Find the indefinite integral by using the appropriate formula

A: Given: ∫cos4xdx   Formula used: cos2x=2cos2x-1   cos2x=1+cos2x2

Q: Compute the indefinite integral, and demonstrate that your solution works by differentiating:…

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

Q: Find the indefinite integral.

A: I  = ∫x sin (3x2) dx          ut    3x2 = t                6x dx = dt              xdx = dt6

Q: Find the indefinite integral using the substitution x = 4 sin(8). (Use C for the constant of…

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Q: Evaluate the integral. (6ex + 7 sin x)dx

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Q: Find the indefinite integral using the substitution x = 4 sin θ.

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Q: In the given equation/s as follows , find the indefinite integral:-   vSee the quaetion as attached…

A: We know that, if, y=arcsecx then, x=secy. We use the above substitution to find the given integral.

Q: Use the Method of Substitution to find the indefinite integrals: a) / te“dt (q

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Q: Find the indefinite integral by using the appropriate formula'. ∫e2x cos 3x dx

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Q: 1 Use SUBSTITUTION to evaluate the definite integral to three decimal places. xp- 2x +4

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Q: Find the indefinite integral using the substitution x = 4 sin θ.

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Q: -1 tanx 4. 1+x?

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Q: Find the indefinite integral by using the appropriate formula   ∫ e−3x sin 4x dx

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Q: :Find the integral for the following functions: - Se3x .sinh(x) dx

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Q: sinh x dx 1

A: The integral ∫sinh-1x dx can be written as ∫sinh-1x·1 dx. Now use integration by parts to evaluate…

Q: Evaluate the integral. (5ex + 5 sin(x))dx

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Q: Evaluate the integrals.∫cos x/sin7/4 x dx

A: The given integral is ∫cosxsin74xdx

Q: Evaluate the following integral using trigonometric substitution. 7x dx (36 + x²)?

A: Then we integrate by substitution

Q: x3 sin(x) dx

A: Solve by integration by parts

Q: Evaluate the following integrals.

A: Given: I=∫012sin-1x1-x2dx                                              ...1 for evaluating given…

Q: Use the Table of Integrals in the back cover of Stewart's text to evaluate the integral 2x sin(x?)…

A: We will use the formula here  2 sinA cosB = Sin(A+B)+Sin(A-B)

Q: Evaluate the integral ∫sinhxcosh(−x)dx.

A: Given integral:

Q: Evaluate the indefinite integral below. 15 dx 1– sin?

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Q: Evaluate the following integral using trigonometric substitution. dx (36 + x?)?

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Q: Find the indefinite integral as indicated. J+7° +7) dx 7x dx%3D dx

A: Topic- Integration

Q: 2r cos x dx

A:

Q: 15 – 5 sin (z) ) dz

A: To solve the given indefinite  integral.

Q: Find the indefinite integral and check the result by differentiation.

A: Consider the given expression as dydx=4x+4x16-x2

Q: Find the indefinite integral f Vx2 – 6x + 5 dx using an appropriate trigonometric substitution.

A:

Q: cos(x* + 2) dx

A: To Evaluate: ∫x3cosx4+2dx Concept: ∫cosxdx=sinx+C

Q: Evaluate the integral.  integral sin 6  x  dx

A: Given ∫sin6x dx We use sin2x=1-cos2x2cos2x=1+cos2x2

Q: Calculate the integral / 4 sinh? (x) cosh? (x) dæ.

A:

Q: '1+ sin x t00 dx x2

A: Given:       ∫π+∞1+sinxx2 dx

Q: Find the indefinite integral using the substitution x = 4 sin θ.

A:

Q: Evaluate the integral, if it exists.

A: Given- ∫-11sinx1+x2dx To find- The value of the above integral. Concept Used- The above integral can…

Q: find the indefinite integral 1十xe dx

A: To find the indefinite integral  integration (6/(1+x²))dx

Q: S sin(2x) dx

A:

Q: Evaluate the indefinite integral, ſ cosh? x dx.

A:

Q: Evaluate the indefinite integral. 5e5z sin(e") dr

A: Given,  ∫  5e5x sine5xdx

Q: Find the indefinite integral using the substitution x = √x√4 + x² dx + C 2 tan(0)

A: SOLUTION-

Q: Evaluate the integral. 9e" sin x dx +C

A: We have to evaluate the integral ∫9ex sin x dx.

Q: Evaluate the integral. (9ex + 6 sin x)dx

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Q: Evaluate the integral sin(x²)dxdy.

A: This is a question from the double integral.

Q: Evaluate the indefinite integral. + 10 sec? x) dx

A: We have to solve

Q: Evaluate the integral. (8ex + 7 sin(x))dx

A: The given integration is: ∫0π8ex+7sinxdx To evaluate the given integral.

Q: For ſ sin" (0) cos (0)d0, use a suitable change of variables to determine the indefinite integral.

A: Given : ∫sin7θcosθdθ

Q: Evaluate the integral |-2x? sin(rx) dx

A: Given,          ∫-2x2sinπxdx

Q: Find the indefinite integral using the substitution x = 4 sin(0). (Use C for the constant of…

A: To find the indefinite integral ∫116-x232dx

Q: Evaluate the following integrals using Trigonometric Substitution: 1. X-1- 16x dx

A: Given integral: ∫x1-16x2dx

Q: Find the indefinite integral by using the substitution x = 4 tan(0). (Use C for the com 4x2 dx (16 +…

A: on solving this we get the

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.