Which of these will represent u in the function * y= sin -1 Vx2 + 3x + 4? Sin-1 а. du V1-u?

Q: sin x dx cos5x b.

A:

Q: 1 Show that L-1{ = (sin hat sin at) s4+4a4, 2a²

A: It is given that, L-1ss4+4a4=12a2sinhat sinat. A partial fraction decomposition of ss4+4a4:…

Q: evaluate using the appropriate method or combination of methods.

A: Use 2sinA*cosB=sin(A+B)+sin(A-B) formula

Q: | sin(6y) sin(8y) dy.

A: we have to solve the integral

Q: Show that J (x) = 2 sin x

A: By definition,                  . Now,  we need to prove the above statement by taking n = 1/2.

Q: Differentiate. y = In Sin x  - 1/2Sin2 x

A:

Q: L[sin bd]- show that

A:

Q: d Prove that (sin-l x) : dx V1 – x²

A: To show that:ddx(sin-1x)=11-x2

Q: Evaluate the integral: 2 sin(3x)cos(3x)dx A B 1 4/6 —— 1 wlr 3 1 - wlw

A: Given ∫π3π2sin(3x)cos(3x)dx

Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: Q1) Show that: (b) (cosx) = -sinx =1+* (a) (1+x) =1+6x %3! (e) (VF) = (d) v1+ tan x

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Evaluate the definite integral. sin x dx -dx J12 I+cos² x

A:

Q: d Prove that 1 da (sin-1æ) = V1 – a? -

A:

Q: Calculate for w-z sin(xy+).

A: The given function is w=zsinxy4+9z

Q: 1 dy sin¬' x If y = xv1 – x² + sin=1 x, prove that 24 – 2

A:

Q: 2. If f"(x) = 4 sin x +16 cos x, f(0) = 6, f'(0) = 1, find f(x) and f ().

A:

Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

A:

Q: What is the integrable form of sin-cos-sin0 d0? 2 A /1 – u² du B Vu²-1 du © : fcomndn cosu du D sinu…

A:

Q: ayfor gen f(x) = cos (2r + (/2)), a = /4 TT

A:

Q: dy Find as a function of x when y = sin°(x) %3D O 1) 5cos (x) 2) 5sin (x)cos(x) 3) 5sin (x) 4) 5cos…

A:

Q: Evaluate 1 ei sin x cosx dx using Simpson rule with h = 20

A:

Q: Q1: show that 1) d/dz [cosz] = -sin z, * 2) 1+tan2 z = sec2 z

A: 1) ddz(cos z)=-sinz2) 1+tan2z=sec2z Results:ddxf(x)=limh→0f(x+h)-f(x)hlimx→0sinxx=1limx→01-cosxx=0

Q: Using the substitution t = tan(), the integral 2 dx sin(x) – 78 cos(x) can be written as dt 39 – t-…

A: To make substitution and re write the given Integral.

Q: Find the most general antiderivative of the function. f(x) = 5 cosx-7 sinx

A:

Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: Q! O show th at [x sin'x + V1-x²] = sin'x sin x

A:

Q: make the given substitutions to evaluate the indefiniteintegrals. ∫√x sin2 (x3/2 - 1) dx, u = x3/2 -…

A:

Q: Evaluate the integral sin x dx (2 + 3 cos x)2

A:

Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

Q: Evaluate x2 dx Select one: on O(sin (2r- 1) + 2(2 (2ain (r) + sin(2si To (stn(2 1I) 2(2r sin(2sin

A:

Q: (a) Evaluate the integral sin* 4x cos3 4x dx

A: a) Evaluate the integral                                 ∫0π8 sin4 4x cos3 4x dx  Let us substitute…

Q: by implicit di f foretiation of sin-(xy) - cos-(x- y) Find -V1- (xy)? xV1-(x- y) ² + V1- (xy)? -V1-…

A: Using Implicit Differentiation

Q: Evaluate in x cos x dx. .3 I COS" T

A:

Q: 2. Use the substitution technique to find [*5'sin(5¹) dt exactly (not an approximation).

A: The given integral is ∫015tsin5tdt use the formulas, ddtat=atln(a)∫sint dt=-cost+C

Q: 2 Given that: J2(x)=-, cos.x + sinx find J(x)

A:

Q: The suitable substitution to evaluate sin 4(x+2) dx is None OA [1-cos8(v+2)] В. [1+ C. 2 + cos8(r…

A:

Q: Q4 Evaluate: f(1- cos²4x) sin4x dx.

A: The given integral is: I=∫1-cos24xsin4xdx   As we know the Power rule. ∫xndx=xn+1n+1+C

Q: 3. If w-f(x.y) and x-r.cose, y-r.sin6 Prove that - A + fy ar

A: Given that w=f(x,y) and x=rcosθ,y=rsinθ Prove that ∂w∂r2+1r2∂w∂θ2=fx2+fy2

Q: 3 Q19- if z =- 4x³y sin sin (x³y) əz find əx

A: We want to find partial derivative of the given function.

Q: Find this second derivative: dz O 2 cos a? – 4x² - sin x² O 4x² cos x² – 2 sin æ² O 82² (cos z²)…

A: Given : Second derivate of sinx2

Q: find integral 2) S sin?xdx dx cos³x

A:

Q: Differentiate each of the f cosh(x)+1 cos(r)+1 a. Y =

A:

Q: Find the deriva tive Of 6- sin (xy)+ e'

A: Note:- It is not mentioned in question for derivative find with respectvto what variable(x or y) so…

Q: Verify that sin(x+y)+sin(x-y)=2sinxcosy

A:

Q: Differentiate implicitly to find 04 0-3 O 3 3 cos(y+z) 4 cos(y+z) Əz Əy 2 given 4x + sin(3y+z).

A:

Q: make the given substitutions to evaluate the indefiniteintegrals. ∫x sin (2x2) dx, u = 2x2

A:

Q: Use Gaussian Quadrature (n = 3) to approximate f(x)dx, where: f(x) = (2.54 - sin0.32x)2 cos0.32x ,…

A:

Q: (x² sin(x')dx = 3 %3D

A: Given : Integration of X2sin(X3)dx