he resulting integral of dx is ax + b ln x -Arctan +C, where a, b, d, e, and x3-2x2+5x are integers. What is the value of b?

Q: dx Evaluate the integral V1 + 9x² 1) Which substitution will change the integral into one of the…

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A: this can solve simply by apply the integration formula

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A: Given: To derive the formula for the volume of the ellipsoid by using a triple integral. x2a2…

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Q: Consider the integral 3 dx V1 – x² If the integral is divergent, type an upper-case "D". Otherwise,…

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Q: Evaluate the integral. (Use C for the constant of i 4x2 + 3x + 4 dx (x² + 1)2

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Q: Q1/ Use Gauss-Legendre formula to evaluate the integral o e-dx withn= 3.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the integral. J 3 x√9 - (In x)² + C dx

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A: We have to evaluate ∫0π1-cos2θ dθ We know that sin2θ+cos2θ=1 ⇒ 1-cos2θ=sin2θ Therefore,…

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A: Topic:- integration

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Q: (d) Prove that 1-cos 2x dx is divergent. Hint: Split the expression inside the integral into two…

A: Integral is converges or divergence

Q: In evaluating x- 2 dx by substitution, if u=x- 2 then what will be the resulting indefinite integral…

A: We can find the answer as below.

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Q: Q2/ Find the integral of, 1/n f(x) * cos(3x) dx , for f(x) =1 on [-n, 0] and f(x) on [ 0, a] (using…

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Q: Choose the most appropriate answer: Evaluate the integral : J 3x2 dx x3+20 O In(x³ + 20) + C T 40) -…

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Q: Evaluate the integral dx (4x + 14) by making the appropriate substitution: u = dæ (4x + 14)* Submit…

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Q: Which of the following integration expression can be transformed into integral of power (Ju"du). 2…

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Q: In evaluating /x V4- x dx by substitution, if 4 = 4 – x then what will be the resulting indefinite…

A: ∫x4-x3dxu=4-x→dudx=-1→du=-dx

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Q: TU 2. fz sin² x cos4 x dx J

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Q: The resulting integral of S dx is In + e Tan"1+ C where a, b, d, and e are integgrs. x+x²+4x+4 What…

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Q: 4 -dx xln?x 00

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Q: The improper integral J 1 r2-4x-5 dx is given by:

A: In this question, we reduced the integral into trigonometric form by using suitable transformation.

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Q: In the indefinite integral J 3x²e* dx, the integrand is A 3r © 3x2 D x³+C B.

A: The given integral,    ∫3x2ex3dx

Q: The resulting integral of form --F(0) +C. de has the What should be the value of e to make F(@)=0?

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Q: Evaluate the integral of ax^2 e^bx dx assume a and b are constants.

A: Please see the explanation below

Q: Evaluate the integral in (7x) -dx. Choose the correct answer below. O A. - In (x) - 16 1 +C 16x* -In…

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Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.