2.1 Given that 1 sinh x show that dy cosh a. dx

Q: 1. Jo cos x sinh x dx

A: Explanation and solution is given below....

Q: 1. Find the following antiderivatives. (a) [² cosh x + 1 sinhx dx

A:

Q: 2. Find the following indefinite integrals. Use Substitution and/or Integration by Parts when needed…

A: a) Evaluate  ∫sinθcos4θdθ         ...(1) Simplification: Put cosθ=t⇒-sinθdθ=dt in (1)…

Q: Given (1) Find dy. by applying implicit dx di fferentiation, in (1) (1) explicitly and Solve eg tor…

A: We use the definition of implicit differentiation of a function to solve the given question.

Q: 4) evaluate the following definite integral: T/2 3 sinx cos x let dx 1 + 3 sin? x

A:

Q: 4. Determine the following integrals 4.3 (a? + x*)cos(2x) dx

A:

Q: S 4x cos(2 – 3x) dx

A:

Q: 1) Find the following integals: 14) S(2? -x) dx le) S x* dx la) S x* dx Ic) )치 dr If) Sdx ax ti

A:

Q: 4) Evaluate the definite integral: S, (6x² – 3x + 7)dx.

A:

Q: 2) Find L{te"sin5t} using two methods. ans: (s+2)2+25

A:

Q: 2 6 Use Fubini's Theorem to evaluate 2x exy dx dy. 00 26 2x e Xy dx dy = | (Type an exact answer.)…

A:

Q: Prove that sinh−1 t = ln(t + √t2 + 1 ).

A:

Q: The integral S³ S S Sse x dx x²+√√x²-1-1 sece tane de sece - 1 cose d 1 - sino sine de 1 + cose…

A:

Q: (4)Evaluate the definite integral (a)[ 1+sin x dx (b) | 2t + cost dt -7/2 5 x + dx (d)[ sec' 0 d0…

A:

Q: e the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+3/x) dx. -dx, 1+x²

A:

Q: 2. (a) | +4 Evaluate the integral. √2x + 1 dx

A: Taking substitution as 2x+1 = t

Q: If we let u = cos t, then the integral [(sint). In (cost) dt can be expressed as - [In(u) du 0…

A: An integral is given. We have to write the substitution form of the integration in terms of the…

Q: (b) Evaluate 1 dx using Romberg's S. 1 + x2 hence obtain an approximate value of T.

A:

Q: 6. Evaluate the integral. S-11 sin x cos(cos x) dx

A:

Q: Jse the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+3/x) 1, dx, 1+x2 I =

A:

Q: 3. (4 pts) Find the exact value of each definite integral. 4x5 dx (b) dt

A:

Q: After integration by parts we have e70 cos(80) d0 e70 sin(80) d0.

A: Explained below

Q: sinh(1+Inx)= Select one: e?x² – 1 2xe None e Inx 2 Zero e?x?+1 2хe x²+1 O 1+ 2x

A: Simple use log properties and simplified put x as ln(ex)    then simplified.. Go through the…

Q: ·S- The integral x dx x²+√√√x²-1-1 can be transformed to which of the following using trigonometric…

A:

Q: .2 -dædy In (x) ey

A:

Q: Prove: ex. a. ſ csch x = In b. S sech x = 2 Arctan(e*) + c

A: a).  ∫cschx dx=∫2ex-e-x dx=∫2ex-1ex dx=∫2exex2-1 dx Put, ex=t⇒ex=dtdx⇒ex dx=dt Therefore, ∫cschx…

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 8 | (- 2* + 20z – 96z?…

A:

Q: Evaluate the following integral.

A:

Q: See images below

A:

Q: Q2]Using Simpsons1/3 rule for evaluation of sinh(e¬*) dx use n = 4 andwork to 5 decimal place?

A: The formula for Simpson's 13 rule is: ∫abfxdx=∆x3fx0+4fx1+fx3+...+fxn-1+2fx2+fx4+...+fxn-2+fxn Here,…

Q: QUESTION 4 witQUTMOUTMOU with respect to r. Differentiate y 3- cosh r 6+ sinhr MO

A:

Q: 6. (a) e' sinht (b) 3e2 cosh 4t

A:

Q: on 1. Complete the following computation a' In(8x)dx via integration by parts f(x) = In(8x) and…

A:

Q: Evaluate the following integral.

A:

Q: 2) Solve the following integrol with details. -21 r3 cos? Oredr sinQdo =x 2 32TT a x=?

A:

Q: Question 13 Evaluate the integral J sinh? (2x)cosh(2x) dc sinh“(2x) +C A sinh(2x) +C B 9 costf(2x)…

A: Use the derivative identity, ddx(sinh(ax))=acosh(ax) And the power rule of integration is:…

Q: 4. Evaluate the following indefinite integrals. (a) / (cos(0) – sec(0) tan(0)) d0

A: Explanation of the answer is as follows

Q: sinh(1 + Inx) = Select one: e?x² +1 2xe O None x²+1 O 1+ 2x O Zero e Inx 2 e?x? -1 2xe

A: To solve  sinh(1+lnx)

Q: 12. By using the trigonometric substitution X = x = ; + sin(0) then the integral S - xp- (3+4x-4x2)…

A:

Q: * /Q20 In(cosh x + sinh x) + In(cosh x – sinh x) %3D 1 -1 2 O Leave Question O

A: The problem can be solved using the logarithmic formulae. The rule for the addition of the term is…

Q: Q2/ Find dy/dx for the following functions: x4 In x - 16 1. у%3D (ln x)3 2. У 4 3. у %3D0 (sin (In6)…

A: y = (ln x)3 To find the derivative (dy/dx) or the given expression we will use chain rule. Chain…

Q: Evaluate the following integral. π/4 1 π/2 SS sin Tx cos y sin 4z dy dx dz 0 0 0

A:

Q: 49. * ccunlı * sinh xdr = In 2 e€u«lı * sinh xdx = A. e - e B. c - c C. ei - e В. D. ci - 1

A:

Q: 2.2 Evaluate following integrals. .sin VT cos E 2.2.1 dx

A:

Q: In 2 cosh x =dr. V sinh? r + 4 sinh x + 2

A:

Q: Q1 Evaluate the following: Ine dx n/3 4 sinx 1- Jo 2- Jo x(Inx)2 3-m 2e*cose*dx in 1-4cosx

A: Simple integration problem.....

Q: Calculate SN given by Simpson's Rule for the value of N = 6. cos(3x²)dx (Round your answer to six…

A: given integral :

Q: 1. Solve the hyperbolic function of the following. i Prove that coshx – coshy = 2sinh (*) sinh ().…

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: