Exercise 4: Integrate the following. dx (a) /= 16 х dr (b) / 5 + 2x4 et dx (c) / 1+ 2e2x cot x (d) CSc x + sin x dx sec2 x T9 - tan? a (e) dx dx (f) TV1- (In a)²

Q: Find dy/dx by implicit differentiation. (cos TX + sin Ty) = 18

A:

Q: Calculate integration | cos -1 1 dx

A:

Q: Integrate: So a sin(x²) dx

A: We have to integrate

Q: Evaluate cos √6x dx using a substitution followed by integration by parts.

A:

Q: 3G)Ú) Show that the reduction formula for atanx で-u sec"x dx = Sec" 「キu ) Hence use tthe formula to…

A:

Q: tan (VT)+2 dx J Va (sec(VT) – cos(/7))

A:

Q: dx S COsxtanx

A: Here we will solve the given integration,

Q: Estimate S, cos(4x)dx with Trapezoidal Rule. n = 10

A:

Q: dy Find by implicit differentiation. dx - 20x = 20 - eY dy %3D dx (Type an exact answer.).

A:

Q: b,c,d

A:

Q: b) Find if Scosy Vt3 + 5 dt + tany = x -sinx b) Find if S* Vt2 + 5 dt + siny = x – x°cosy dx2

A: Solve by differentiation

Q: TT sin 5. Approximate dx by Simpson's rule with seventh ordinates?

A: Simpson's Rule:    ∫abf(x)dx=∆x3f(x0)+4f(x1)+2f(x2)+...+2f(xn-2)+4(fn-1)+f(xn) Where, ∆x=b-an We…

Q: 3. Integrate the following dx (i) V9 – x² (ii) ſe-3*cos4x dx (iii) ſ sin³2x dx -

A:

Q: find dy / dx by implicit differentiation.

A:

Q: arctanx e dx (1+x²,"

A: The given problem is to evaluate the given integral. We have to evaluate by using substitution…

Q: dy Find by implicit differentiation. 20x = 20 - ey ... dx (Type an exact answer.)

A:

Q: valuate the triple integral ***"* sin² (z)ze-²v³ dzdyda

A:

Q: c) Use trigonometric substitution to integrate dx 4-x2

A:

Q: dy dx a) { In |0* + 1|} „b) arctan (ve2 -1) , c) sec-(0²) – 1

A:

Q: V3x d. Evaluate dx sin(3t) dt

A:

Q: sinx D.a) Find if mx Vt + 5 dt + siny = x-x²cosy

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

Q: Tutorial 14 If y = (sin-1 x)², show that dy (1 – a²) - dy = 2. dx dx?

A: Given, y=sin-1x2 Differentiate with respect to x y'=2sin-1xddxsin-1x=2sin-1x11-x2y'=dydx=2sin-1x1-x2…

Q: 2. Use implicit differentiation to find dy/dx: e"y+ In(arcsin 2y) = 3ª ln y + 5.

A:

Q: Estimate 1 7 cos(x2) dx 0 using the Trapezoidal Rule and the Midpoint Rule, each with n = 4. (Round…

A: I=∫017 cos (x2) dx             f(x)=7 cos (x2)b=1, a=0, n=4h=b-an=14=0.25aThe Trapezoidal…

Q: S tan ax secex dx 3

A:

Q: Integrate: / cos“ x dx

A: The given integral is: I=∫cos4x dx Reduction formula: ∫cosnx dx=1ncosn-1(x) sin(x)+n-1n∫cosn-2(x) dx

Q: find dy / dx by implicit differentiation.

A: Implicit differentiation is performed when the dependent variable cannot be explicitly written as a…

Q: e ln (xle) (2– sec²r)cm#/c°sec³x sec(3A – x) What should be the value of A for -dx to be integrable…

A:

Q: Describe the method used to integrate sinm x cosn x, for m even and n odd.

A: Method to integrate sinmx cosnx ,for m even and n odd. Let m=2k and n=2k+1 ∫sinmxcosnx…

Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your du? du = x…

A:

Q: ■ Find dy /dx  by implicit differentiation 4 cos x sin y =1

A: To find dy/dx

Q: Find dy/dx by implicit differentiation. (cos TX + sin ny)8 = 26 sin (7)x cos(7)y dy/dx =

A:

Q: Grade: 107.5/156 Print Version dy sin(5æ) Find for y dx dy Preview ||

A:

Q: From the figure formed in integrating -dx, what is the term or value that is adjacent to the angle…

A: Given:    ∫x2-3xdx

Q: In integrating the function f(3x + 5)(cos ) dx using integration by parts, what would be your du?

A:

Q: In integrating the function fx In 5x dx using integration by parts, what would be your v?

A:

Q: dy/dx=(x+siny)/(2y-xcosy) is an exact equation

A: Given that dydx=x+sinyy-xcosy we need to check that it an exact equation

Q: lel sin(mx) sin(nx)dx=0 (a)

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: - y = sin² (3*)

A: We have to find derivative of given function.

Q: Siny dx t sin Zydy + x dy

A: To solve: sin⁡ydx+sin2⁡ydy+xdy=0…

Q: Find at the point (1,0) for cos xy + ye* = 0. dx

A:

Q: In integrating the function f(3x + 5)(cos) dx using integration by parts, what would be your v? v =…

A: The integration by parts is done using the formula: ∫udv=uv-∫vdu. In general, the ILATE rule is used…

Q: Find dy/dx by implicit differentiation. (cos TX + sin ny)³ = 26 dy/dx =

A: Differentiate above equation with respect to x

Q: Find dy/dx by implicit differentiation. sin x + 2 cos 2y = 1

A: the given implicit function is: sinx+2cos2y=1 we have to find dydx by implicit differentiation

Q: Find dy/dx by implicit differentiation. 5+ 5.x = sin (ry²) dy/dx = %3D

A: Given that,   5+5x=sinxy2

Q: Consider the implicit function. ev = sin (2x) dy in terms of x. dx Determine the formula for dy dx

A:

Q: 2-€2x y") edxtcuxe yd-siny)lye.co

A: A differential equation of type   P(x,y)dx+Q(x,y)dy=0   is called an exact differential…

Q: Cualuate the definle integial. x33 COs (xH) dx

A: