Chapter 6, Section 6.3, Question 006 Use the Fundamental Theorem to evaluate the definite integral exactly. Enclose arguments of functions in parentheses. For example, sin (2x). Equation Editor Ω Common Matrix sin(a) cos(a) tan(a) qb d. ab sec(a) cot(a) csc(a) fdx dx la| va sin- (a) cos (a) tan- (a) 00

Q: in−1(x) + cos−1(x) =  ? 2

A: Given that : The equation is sin-1 (x) + cos-1 (x) = π2 .

Q: Find the arc length of the curve y = x²/2 from x = 0to x = 1(Figure 7.4.4).

A: Arc length of curve y = f(x) is, L=∫ab1+dydx2dx

Q: At a certain moment, a race official is watching a race car approach the finish line along a…

A: At a certain moment, a race official is watching a race car approach the finish line along a…

Q: * DeMoivre's Theorem 4 (4(os 30 + ) i sin 30

A:

Q: To evaluate the integral sin ³0cos (A) sin²0=1-cos²0 1-cos20 B sin ²0 2 sin20 sin cose 2 1+ cos20…

A:

Q: Chapter 6, Section 6.3, Question 012 Use the Fundamental Theorem to evaluate the definite integral…

A: Given,

Q: Chapter 6, Section 6.3, Question 004 Use the Fundamental Theorem to evaluate the definite integral…

A: To evaluate the given definite integral.

Q: Find the limit.

A: Consider the given limit lim△x→0sinπ6+△x-12△x   Use the formula  sinx+y=sin x cos y+cos x sin y…

Q: Express the 10th term of ( x1 + x2)º in terms of sinusoidal functions (sin, cos).

A: The expression is x1+x220. As we have obtained…

Q: ) A)= show that sn A-esA z|-Sin 2 A exact value of Sinis- losis Hence. find. the.

A: i To show that, sin A-cos A2=1-sin 2Aii To find the exact value of sin 15°-cos 15° by using the…

Q: 32 Question * (3 Points) The proper transformation for sin²x to make the f sin²x dx readily…

A: substitution

Q: cos 2x +1 Prove that sin 2x

A:

Q: Find the maximum value of sin θ + cos θ.

A: Let  fθ=sin θ+cos θ Differentiate with respect to 'θ', we get f'θ=cos θ-sin θ For maxima or minima,…

Q: Solve if the set of functions (1, x, sin x, e^x, cos x) is linearly independent or dependent…

A:

Q: Section E: Integration of trigonometric functions - 2 sin x 7. - dx cos x 8. sin 4x cos 4x dx

A: In this question, we need to solve the given integrals.

Q: 41-44 Use Theorem 13.5.3 to find dy/dx and check your result using implicit differentiation. 41. x²y…

A:

Q: Consider the ODE: (2x siny)dx + (x2² cosy + cosy)dy = 0 a. Solve the ODE by separation of variables…

A: We have to solve ODE by seperation of variable

Q: sin (21 + 1) dt J cos² (21 + 1)

A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: sin(1) dt Using an appropriate substitution, evaluate: [2+ cos(t)]* A +C 3[2+ cos(t)]3 3 B +C [2+…

A:

Q: Locate and identify the absolute extreme values of cos (ln x) on [1/ 2, 2].

A:

Q: evaluate

A: Given integral is evaluated as follows.

Q: Calculate fsin³ a cos° a dx.

A: Let cosx = t Differentiate on both side   - sinx. dx = dt    sinx. dx =  - dt

Q: Question 004: Complete the following question involving Integratin by Parts Method. Given the…

A: the given integral is ∫4x*sin5x dx and the substitution information is: u=4xdu=4dxv=-15cos(5x) we…

Q: Chapter 6, Section 6.3, Question 014 Use the Fundamental Theorem to evaluate the definite integral…

A: Given,

Q: (1+ etane) sec² e de = e TO FO 2 [0(sin(In 0) + cos(In 0))] = de csc(ln 0)

A: ∵1     ∫0π4(1+etan θ) sec2θ dθ=∫0π4(sec2θ+etan θsec2θ )dθ=∫0π4sec2θ dθ +∫0π4etan θsec2θ dθ∵∫0π4sec2θ…

Q: Question 2 Evaluate x cos(3x) dx. .2 x° CoS Question 3 Evaluate e" cos (2x) dx. Question 4 Evaluate…

A: According to the guidelines issued by the company We are supposed to answer only one question.…

Q: 5. म 4-93ो डे (A-कर कर Cos (4-3x) dx

A: ∫sin54-3xcos44-3x dx=∫sin44-3xcos44-3x sin4-3x dx=∫sin24-3x2cos44-3x sin4-3x dx=∫1-cos24-3x2cos44-3x…

Q: Question 4 Calculate the given integral: / tan (4x) dx 1 1 a) 능 -tan(4x) + 4x + C tan’(4x) + 12 1 b)…

A: We have to solve the integral

Q: tan x 4. a) Evaluate dx. In (cos x) b) Evaluatef e4*x3 dx.

A:

Q: 450 400 AA 350 300 250 200 150 100 50 -4 -50 8 16 24 28 36 12 20 32 -100 -150 -200 -250 -300 Dy =…

A:

Q: Question 3 3. Evaluate 2 dr. sin Upload Choose a File

A: Here we have to evaluate 3)  I=∫sin2xsinxdx

Q: · /9" cos(1 – f') dt 17. 9t" cos

A:

Q: 9. cos x dx

A:

Q: Solve the equation below. (cos x – 1)(2 sin x + 1) = 0 if 0 sx< 2n. %3D

A: Given: cosx-12sinx+1=0 Solve the expression for x. cosx-1=0cosx=1x=cos-11x=2nπ

Q: Part 3 Establish the identity. sec 0 CSc 0 %3D sec 0-1

A:

Q: Establish the identity.

A:

Q: Verify the identity. 2 cs" e 1-- 1+ sin 0 = sin 0

A:

Q: Section 2.6: #2) Find dydk by tmpHet differentiation- Cos Cxy) = 1 + Cin COs

A:

Q: Exercises (12): 1. Can Rolles theorem applicable for the function y = sin3x in [0, ] If then find…

A:

Q: Find (algebraically) the absolute maximum and minimum values of f(x) = cos² x+ sin 2x on [0, 5), if…

A:

Q: Chapter 6, Section 6.3, Question 013 Use the Fundamental Theorem to evaluate the definite integral…

A: Consider the integral

Q: The x2-4 dx can only be evaluated using trigonometric substitution technique. A True False

A:

Q: у%3D sin(4x — 2) cos (4x + 2) || -

A: topic - derivative

Q: f₁(x) = 9, f₂(x) = cos²(x), f3(x) = sin²(x) linearly dependent linearly independent

A: Here given  functions are.  9. ,Cos2x  , sin2x

Q: Activity 2 Differentiate the following. 1. y = sin(6x) 2. y = sin (5x – 2) 3. y = tan (2x³ + 5) 4. y…

A:

Q: Prove that 3x Question 4 (i) sin(tan-(3x)) cos(tan-(3x)) = 1+ 9x² d 1 (ii)- sin-'(/) = dx 2a/1 – x

A: A detailed solution is given below.

Q: Chapter 6, Section 6.3, Question 009 Use the Fundamental Theorem to evaluate the definite integral…

A: Consider the given integral.

Q: Prove the identities: (x sin 0 – y cos 0)² + (x cos 0 + y sin 0)² = x² + y²

A:

Q: Evaluate: tan(4x +3)dx A 4 A -In |cos (4x + 3)|+c B -In |sin(4x + 3)|+C 1 (c) -In |csc (4x+3)|+C D…

A: Integral calculus is the fundamental discovery was the link that exists between this and the…

Q: To evaluate the integral 1 sin20 A sin cose= 2 1-cos20 B sin²0= 2 1 + cos20 (c) cos²0=- 2…

A: In this question, we want to know which identify is useful to solve the Integral.