(ii) Using (i) evaluate in terms of x. (i) Use a suitable u to prove that S cos √x = 2 = 2 fue S u cos udu. cos √xdx

Q: Integrate S(cos x)e*+sin xdx B. et-sinx + C A. -e4+sin x + C c. e4+sinx + C D. e-4+sinx +C A В C D

A: Given: I=∫cosxe4+sinxdx  ....(1)   We know that; ∫eax+bdx=1aeax+b+C

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A: I have stated the used formulas in the solution.

Q: Evaluate [sin³ a x cos x dx. + C

A:

Q: Use the method of substitution to evaluate 2x sin x? + c 2 sin x? + c sin x? + c 2 – sin x² + c

A: As we know that the common integration of : ∫cosudu=sinu ∫a·fxdx=a·∫fxdx

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A: we have to use substitution method to solve this integral. these are basic integral formulae which…

Q: [0,2m] find ao for f(x)=cos 2° 其bO 2n.c0 0 d O x/2

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Q: | (cos c+ 1) dc;let x be constant

A:

Q: The function y = 2x – cos x have two variables (x and y), these variables called

A: Here, the given equation is y=2x-cosx , which is a function of two variables(x and y). The name of…

Q: fsin²7x dx Select one: O a. O b. O c. O d. O e. 7x - sin²7x cos 7x 14 7x sin7x cos 7x 7 7x + sin7x…

A: Formula used

Q: | (2æ – 9)sin (a? 8) dæ = Evaluate 9ж + - Include all steps in your written work.

A: The given integral,∫052x-9sinx2-9x+8 dx

Q: Evaluate L{t°e! e3(1 – t) 3e-t sin (4t - 2) 2) + t2 $ (3t)} cos

A: Explanation of the answer is as follows

Q: Rewrite cos x + 3 in terms of sin(x) and cos(x). COS

A:

Q: n/2 1+2cos x Q:Evaluate: dx. (2+cos x)*

A:

Q: 4 cos z Evaluate S 16-y2 ydxdydz

A: To solve the given triple integral ∫0π∫04cosz∫016−y2ydxdydz…

Q: 12. Evaluate: 212-3V+1 (a) (d) / sec (2) / (b) / sec (20) de dr 1 (e) rVI-1 dr dr 16+9r2 (c) sin t…

A: The given integrals are; (a) ∫2x2-3x+1x2dx (b) ∫01x16+9x2dx (c) ∫0π/6sintcos2tdt

Q: 5. Using the expressions of J₁/2(x) and J-1/2(x), express the following in terms of sinx, cos x and…

A: Bessels function Values We know that  J12(x)=2πxsinxJ-12(x)=2πxcosx Also, we know that…

Q: 2c. Show that * (5 - ) 4 sin z - cos 2r + 3 -8 cos for every r.

A: To prove: 4sinx-cos2x+3 = 8cos4π4-x2 We know that cosx-y  = cosxcosy+sinxsiny and cos2x= 1-2sin2x

Q: sing the relation r = Vn show that J_1(x) = COS X

A: We have to proof that given relation

Q: 3. Evaluate f x sin2 (x²) dx.

A: Given I=∫x sin2x2 dx To Find I

Q: Let F= (2e", 5 sin(x), 8 cos(x)). Calculate div(F) and curl(F). (Use symbolic notation and fractions…

A:

Q: Find all xE[0,2pi] that satisfy sin 2x + cos x = 0 x =

A: Topic- Trigonometric Equations We are given, sin(2x)+cos(x)=0 and x∈[0,2π] We know that sin(2x)=2sin…

Q: Evaluate dx 9. x2 |1 4x2

A:

Q: c) Evaluate Ssin 3xcos 4x dx by using integration by part.

A: Given integral is: I=∫sin3xcos4xdx Simplifying it:…