(-1)*+1 bn x sin nx dx || n -ㅠ

Q: Use the accompanying figure to show that 7/2 sin x dx sin 'x dx. 2 y = sinx 1 y= sin x 1

A: Given: To prove, The given graph is shown below,

Q: Show that for n > 2, tan x sec"-2 п — n-2 T dx . sec" x dx sec"- п — 1 п — Use this to find sec x…

A: ∫sec4x dxWe need to find the integration by using the given formula.

Q: 8. What is dx (x2+8)3 9. What is {(Sin (tan (x*)} dx dy 10. What (x -2x +5)6 dx =一

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Q: Evaluate the integral | tan° 2x dx 5

A: Solve the given integral.

Q: 24 dx Evaluate 1- cos (8x) 24 dx 1- cos (8x) | I3D

A: Using trigometric identities

Q: 5. y = tan- (a) 6. y = 4x sin (3x - 9) 7. y = sinh (4x – 1)

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Q: 4si 2xcos²x dx sin2xcos2x

A: It is given that,     ∫4 sin2xcos2xsin2xcos2x dx We have to evaluate it.

Q: 1 (7 – x²) sin nxdx An 2(-1)"+1 n3 II

A: Integration by parts  ∫U·Vdx =U·∫V dx-∫dUdx∫V dxdx Where U and V are the function of x . Also,…

Q: Find y' i. y = sin(2x² + tan(6x² – x)) ii. y = sin(2x² + tan(x – 1))

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Q: | – (3x² sin x + 2) dx In r dx Je

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

Q: Write ∫ tan2k+1 x dx, where k is a positive integer, in terms of ∫ tan2k−1 x dx.

A: Given integral is ∫tan2k+1dx. Rewrite the above integral as follow.…

Q: 1 x³ y =e*(dsin²3x-tanx ) - 10 y'=? (fх +1)

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Q: sinx-1 V(1-x2 dx

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Q: 4. sinx 1-sin² x dx

A: We have to find the value of the given integral ∫sinx1-sin2xdx

Q: 2r sin 1 (r²) d»

A:

Q: b. S(5 tan 3x – 2 sec? x)dx S 3xvx – 4dx C.

A: To integrate the given functions.

Q: Evaluate the following 1, intergral from 0 to π/2 of (Cosx)/(1+sin^2x) dx

A: As per bartleby guideline for more than one question asked only first is to be answered please…

Q: sin 2x dx /2 cos 2x

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Q: Determine the sum of the coefficient/s when we evaluate (sec(x) – tan(x))²dx.

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Q: 3 2 1. + cos x) dx x3

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: (A very cute proof ) I want you to show using integration by parts that sin(mx) sin(nx) dx = 0 if m…

A: To show: ∫0πsin(mx) sin(nx) dx = 0 We know that, Integration by parts ∫u dv = uv - ∫v du Suppose, u…

Q: 90 V sin(x) dx V sin(x) +v cos(x)

A:

Q: (b) 는(cosx)=-sinx (d) VI+ tan x 1+* Q1) Show that: (a) (1+x) =1+6x (e) (V): *- () %3D

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Q: 2) Solve for r; 0 < x < 2n. cos r + sin r tan r = 2

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Q: /2 Evaluate : | sin x dx. -/2

A: For the detailed solution of the problem follow the next step.

Q: 4 The range of y =sinx for 7SXS is 2 0syso 4 <ys0 sys1 ys 4 -1sys,

A: We are given a function y(x) = 4/5 sin(x) and we need to find the range of y(x) when π ≤ x ⩽3π2 (…

Q: What is the antiderivative of sin^2(x) + 2sin(x)?

A: Antiderivative of sin^2(x) + 2sin(x) is given by,  ∫[ sin2x + 2sinx ]dx =∫sin2x dx + ∫2sinx dx

Q: What is the antiderivative of  2(sin(2x))/sin(x)?

A: The anti-derivative of a function is a differentiable function whose derivative is equal to the…

Q: sin ydy (4 + cos y)²/3

A: We know that integration of xn is xn+1/n+1 +C. Here C is integral cosntant.       Here i attached…

Q: Evaluate: S 0 tan¬(0)d0 arctan(8)–0 Sarctan 0 + C 2 arctan(0) 0 zarctan 0 + C 2 arctan 0- 0…

A: Please refer the attached image for complete solution.

Q: 19. Evaluate using u-substitution: S tan6x sec² x dx

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Q: sin(1/n) n=1

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Q: l6X-tan 3X, (- find openint & concav f(x)= 6-(seč 3x)3 3 sec?

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Q: Evaluate the integral. 1/2 3 sin 2nx dx 2.3 16 16 3 8

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Q: Evaluate the ff. 1.  ∫(3x+4)^2 dx 2.  ∫ sinx + sin(π/2-x)/cos x dx 3. ∫(1-r) √r dr

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Q: • TT/3 1– sinx' |dx From right endpoint 1- cscx + n = 4 n/4 coS X

A: We have to find the right end point of the following expression   The given expression is  we…

Q: D Sin 2x 46 4 Sin -3 = -3%3D

A: (a) Given trigonometric equation is: sin 2x = 4 cos 2x We have to find the general solution.…

Q: tan(x) dx sin (x) + cos4(x)

A:

Q: 1) Completely integrate the following: f sin*(3x) dx

A: Let ,I=∫sin43xdxPut 3x=udifferentiate 3dx=dudx=du3I=∫sin4u13duTake the constant out:…

Q: (x² cosh(sin(x – y) 8.

A: We have to find the partial differential with respect to x in question number

Q: 3. "sin 2x dx [²sti answer: dx answer: 2+4

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Q: I. Power Formula cosh3x dx 1. S (1+2sinh3x)5 tanx dx 2. S (1+Iпcosx)2 3

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Q: dx |2 sin 2 sin x — сoS X

A: I have appended the formula used in the solution part

Q: Find sin' (2r)dz . - 능 cos"(2z) 글 cos (2x) + - cos (2x) + c Check your variables - y

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Q: cos2x – sin2x cos2x F(x) +C. What is F(M)? For dx%3D cosx – sinx 3

A: A detailed solution is given below

Q: 4 4. (x2 – 5x + 10)dx 10 x dx x2 5. 6. (2x + sin x) dx

A: Given:4.∫1 4x2-5x+10 dx5.∫510 x8x2 dx6.∫0π2 2x+sinx dx

Q: 3 sin x d.x 4 1. Show that

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Q: Find y' i.y = sin(2x² + tan(6x² – x)) ii.y = sin(2x² + tan(x – 1))

A: We have to differentiate the given functions

Q: |x sin x'dx 7.

A: