In solving for the antiderivative of f(x) = V94X- x2 using trigonometric substitution, Jf(x)dx is transformed into after appropriate substitution. Determine the value of (e) for 0 = 1.85. (note: 8 is in radian, your answer must be in two decimal places )

Q: Consider the series Σ 1+ 6n n=0 If we let f (x) = then f f(r) dr %3D 1+6 x O is finite. O is not…

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Q: Question 17 sech (Insinx) cotxdx ==2tan-' (sinx) + C A) True B) False

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Q: Determine whether the function is one-to-one. If it is, find a formula for its inverse. f(x) = x +7…

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Q: Evaluate: Je*cos(7e*)cos(4e*)dx.

A: We need to integrate∫excos7excos4exdxSubstitute ex=tDifferentiate x w.r.t texdx=dtThen∫cos7tcos4tdt

Q: 1 csch2zdz=-In csch2z – coth2z +C 2 A True B) False

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A: The table shows the result of a survey of 400 authors by a publishing company. Based upon the data…

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Q: 7-4 dt 1.

A: We need to evaluate integral.

Q: x/4 The definite integral sin24x cos2x dx is equivalent to x/2 1 -sin20 cos20 de A x12 2sin20 cos40…

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Q: dx The antiderivativeof |- - 5ln +C. x +5 (A True B) False

A: To find if the given antiderivative is correct or not.

Q: 5 sin e cos ede 2. J sin? 0 +3 sin e – 4 2.

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Q: Insec2 (sin2y) dy e Which of the following is one of the correct steps to evaluate the sec2y

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Q: V20 and that angle A is in Quadrant II, find the exact value of tan A in simplest radical form using…

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Q: then udu = – xdx.

A: Follow the procedure given below.

Q: that

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Q: and that angle A is in Quadrant IV, find the exact value of csc A V91 10 Given cos A : in simplest…

A: The objective is to find the exact value of cscA.

Q: Which of the following is one of the correct steps to evaluate cos³ dt to obtain the correct…

A: In this we have to find which of the following correct steps to evaluate the given Integral.

Q: e4x dx ? (4e2x + 9)/2 Which of the following trigonometric substitutions is the most appropriate to…

A: integration if it is helpful please like it

Q: To begin evaluating sin*x cos°x dx , express A cos x to (cos?x)cosx and use the identity cos?x=1-…

A: We have to use option (A) cos^5x to (cos^2x) ^2

Q: To evaluate sin*2x cos 2x dx , the identities to be used is/are: 1+ cos4x A sin4x & 2 2 B cos²2x= 1-…

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Q: To begin evaluating sin*x cos x dx, express 1+ cos2x cosx to (cos?x)^cosx and use the identity…

A: We have to find out

Q: 3. lim f(x) = x³ - 1 %3D X 1 х-1 X approaches 1 from the left- -x approaches 1 from the right 1.001…

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Q: Question 9 x2 – 4 dx Evaluate: ,2 - 4 + sec C %3D В Vx2 – 4 + 2 sec® + C © =2/ x2 – 4 + sec -1 +C D…

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Q: 1 Which of the following is the antiderivative of f (x) = (x+ 2). ? - Vx + 2 = « (1n (\ &a+ 2+1) +…

A: To find the antiderivative.

Q: © J tane x*dx Using trigonometric substitution technique, the simplified integral after substitution…

A: sec2(x)-1= tan2(x)

Q: 2x+3, x<1 f(x) dr if f (x) = 5, Evaluate -3 A 21 B 19 28 16

A: fx=2x+3,x&lt;15,x≥1

Q: Given sec A = and that angle A is in Quadrant I, find the exact value of sin A in simplest radical…

A: Topic = Trigonometry

Q: Question 18 -미ch2e-coth2e|+C csch2zdz = A) True B) False

A: A detailed solution is given below

Q: dx Using half-angle substitution, the integral is equivalent to 2+ sin x dz A 1+z+z? dz (B (1+z)? ©…

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Q: Find the vector PQ × PR if Р%3 (7,7,0), 0- (1,7,—1), R = (3, 2, –4) (Give your answer using…

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Q: Find the vector PQ × PR if P = (2, 1,0), О %3D (1,5, 2), R = (-1, 13,6) (Give your answer using…

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Q: Evaluate: Scos 2xdx cos2x, cos 2x +C A 2 6 sin2x sin32x +C 6. B 2 cos2x cos 2x + C 6. 2 sin2x,…

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Q: 3. Solve the initial value problem. Determine the interval in which the unique solution of the…

A: First we divide the given differential equation both sides by x2 and then campare it with y'+Py=Q…

Q: 2. Find the unit vector in the direction of

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Q: sech (Insinx) cotxdx=2tan-(sinx) +C A True B) False

A: Solution: ∫sechlnsinxcotxdx =2tan-1(sinx)+C

Q: The result of the integral in 0 given |V y²– 25 -dy is 5 tane – 50 +C, y (A) True (B) False

A: To solve the following integral

Q: sin2x cos3x dx = sin5xdx - sinxdx A True B False

A: Please see the answer below.

Q: Consider the alternating series (-1)"bn with n=0 1 bn 9+ 5n2

A: answer is in next step

Q: To begin evaluating sin*xcos xdx conveniently, express: 1 A cos x as (cos?x) ²cosx and use the Half…

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Q: If h(x) = cosxdx and h =4, then h (0) is equal to 4 | (A) - 4 B None 3 D -3 (E 4

A: Explained below

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Q: To evaluate sin*2x cos 2x dx , the identities to be used is/are: sin4x, 1- cos4x A 2 B cos²2x=1-…

A: Solution:-  This types of trignometric integrals can be solve by reduction formula of integral.

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A: Trigonometric substitution for x2 - a2  is x= a sec(theta)

Q: A (2+35) + 2+j 1-j

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Q: dx is 2/x – Sin|/x +s|+c. Vx +5 The antiderivativeof | - A True B) False

A: To find the antiderivative of the function

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A: A detailed solution is given below

Q: Question 12 is 2V5 – Sin|Vã + s| + C. Vits dx The antiderivativeof |- 5ln x +5 A) True B False

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Q: The definite integral sin24x cos2x dx is equivalent to x/2 (A -sin²0 cos²0 d0 2 x/2 В 2sin20 cos40…

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Q: x4dx Using trigonometric substitution technique, the simplified integral after substitution 4 @…

A: ∫x4x2-4dx=∫x3xx2-4dxLet θ=arcsec12x.=∫ 16sec5θdθ