Evaluate the improper integral or show that it diverges: 00 (a) xe dx 7/2 (b) tan x dx

Q: Evaluate the integral. sin dx Se √1-x² 2

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Q: Use the indicated substitution to evaluate the integral.

A: Given: ∫121dxx2x2+4

Q: Evaluate the integral. ∫ (x -1) Sinπ x dx

A: Let us assume u and dv

Q: Evaluate the integrals ∫tan5 x dx

A: I=∫ tan 5x dx =∫Sin 5xcos 5x dxLet cos 5x=t-5 sin 5x dx=dtsin 5x dx=-dt5

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

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Q: dx sin 3x cos 4x

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

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Q: Evaluate the integral -6 tan (x) dx

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Q: Evaluate the integral or show that it is divergent.

A: Given: An integral

Q: [(x-1)sin zxdx

A: Given:  Let I=∫x-1sinπx dx To Find: To evaluate the given integral.

Q: Use the Table of Integrals to evaluate the integral.  ∫ x Sin( x2) Cos (3 x2 )dx

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Q: Evaluate the integral. ∫ tan3 x Sec x dx

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Q: In evaluating the indefinite integral / sin x cos x d , the appropriate u – substitution and. the…

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Q: dx 2+2 sinx + cos x

A: Given that the integral ∫dx2+2sinx+cosx. Evaluate the given integral. Formulae used:…

Q: Evaluate the indefinite integral.

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Q: x sin¬1 x² 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: use a geometry formula to find the exact value of the definite integral  lxl dx on the interval…

A: Line AOC represents the graph of y=mod x in interval [-2,1]. Here coordinates of 0 are (0,0), A are…

Q: Show that (In kx) dx (In x), where x > 0 and k is a positive dx real number.

A: ddxln kx=ddxln x, where x>0 & k is a positive real number.

Q: Consider the indefinite integral 26 dx: (x7 + 6)"

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Q: Evaluate the improper integral |. 3.x dx or show that it diverges. +1 x?

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

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Q: Evaluate the integral or show that it is divergent.

A: Given: I=∫2∞dxxlnx                           ..1 for evaluating given integral, we substitute lnx=t…

Q: Evaluate the integral.

A: We have to evaluate the integral: ∫1-sinxcosxdx We will use following special integration formula:…

Q: Evaluate the integral x² tan-x dx

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Q: Use the Table of Integrals to evaluate the integral.    ∫et sin (α t- 3) dt

A: To evaluate I=∫et sinαt-3dt

Q: Evaluate the improper integral or show that it diverges. 9. S- dx 0 (20 - 4x)

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Q: Determine if the integral converges or diverges by comparison.

A: We know that sinx lies between -1 to 1. So, Using this we get:

Q: Evaluate the integral.  integral sin 6  x  dx

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

Q: Evaluate the integrals. x√√1-x² dx a. x X b. I si sin5 -cos-dx 3 3

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Q: Evaluate the integrals. ∫dx/(tan-1x)(1 + x2)

A: we have to evaluate the given integral: ∫dxtan-1x1+x2 let the given integral be I. therefore,…

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

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Q: Evaluate the integral of (x^2)sin(x^2) dx as an exact answer.

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Q: Evaluate the integral. x sin(2x) dx = +C

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Q: Use the Comparison Theorem to determine whether the integral is convergent or divergent. sin? x dx…

A: Given the given integral is ∫0π28sin2xxdx

Q: Use U-Substitution to evaluate the indefinite integral. S(5x + 2)?dx S 2x sin(x²) dx

A:

Q: Evaluate the integral using an appropriate method. T/3 x sin(3x) dx

A: ∫0π3x sin(x)dx

Q: Evaluate the integral. integral 0  to pie /2    cos x + sin x dx

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Q: Evaluate the improper integral or show that it diverges. (1+4x)e*dx

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Q: Evaluate the improper integral or state that it is divergent. dx 23) x2 - 25

A: Consider the improper integral  ∫6∞dxx2-25  from the indefinite integrals,         ∫6∞dxx2-25 =…

Q: evaluate the definite integral.

A:

Q: Determine whether the following integral is convergent or divergent. 2+ sin x dx. x² + Vx

A: Given improper Integral ∫0∞2+ sin(x)x2+xdx=∫0∞2x2+x+sin (x)x2+xdx…

Q: Evaluate the definite integral. dx x(1+ In æ)

A: Explained below

Q: Evaluate the integrals. ∫(tan-1 x)5/(1 + x2) dx

A: We have to evaluate the integral: ∫tan-1 x51+x2dx This integral will be solved by substitution…

Q: Evaluate the integral ( sin(In(2+2x)) x+1 dx

A: Given: ∫sinln2+2xx+1dx

Q: Evaluate the integral.

A: Our Aim is to evaluate the integral given below:-I=1[cos(x)-1]dx     -(i)

Q: Evaluate the integral: J sin (4x) dx.

A:

Q: Evaluate the integral - dx · 1- sin x cos X

A: The given integral,       ∫cos x1-sinxdx

Q: Evaluate the integral.  integral sin 9  x  dx

A: Given ∫sin9xdx

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.