dx 8. Find the definite integral Ans:

Q: Q17: Find the indefinite integral: Sezt (e2x + 1)° dx

A:

Q: Find the indefinite integral.

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: Using dy 3 =dx and dx = 0.03, what is dy whenx = 2? 2V3X – 2 dy i (Write as an exact decimal.)

A:

Q: -sinh(x) at x = 0 is dx21 Answer:

A: Derivative of the function

Q: Find the exact value of the definite integral below, using the substitution u = x - 1²/1. X (√6+√2)…

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Q: Find the following indefinite integral. Use C for the constant of integration. VI + 3 V) dx Answer

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Q: Find for the following function: dx 1- y = sin-1 V2x + 3 2- y = 3cot(cosx) 3- v = r?y at r = 1

A: AS PER GUIDELINE WE HAVE TO SOLVE THREE SUBPARTS

Q: I. Evaluate the following integrals. Check by differentiation. S sin 50 cos 50d0

A: Given;            ∫sin 5θ cos 5θ dθ Apply u-substitution: u=cos 5θ⇒du=-5 sin 5θ dθ            =∫-u5…

Q: (- + =) dx when evaluated is equal to 3Vx, 11 Find the value of a. The definite integral 12

A: Given problem:- Th value is given as  ∫49-xa+13xdx=-1112 The integration formula is expressed as…

Q: Q3/ Choose the correct answer to evaluate the following integral 1 dx I = 1 (1 – x+)Ź

A:

Q: Evaluate the definite integral (exact value): 0. dx = -1/4 V 16 x + 8 x +2

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Q: Find the indefinite integral. (Use C for the constant of integration) S cos h² (x – 7) sin h(æ – 7)…

A:

Q: I Evaluate the following expressions by basic integration: dx 2. ,(x + 3)(x – 4)dx

A: Given

Q: dy about cosx +y lny= 0. dx Ask for

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Q: 211 sin nx dx [ [1-cos2nx]dx t, where n %3D

A:

Q: Find the value of following the integral: ☎ COS²T -π1+a* S². dx,a>0

A:

Q: Evaluate the integral sin (y²) dy dx.

A: The given problem is to evaluate the double integral, we have to change the order of integration and…

Q: Use substitution to evaluate the indefinite integral | cos³t sint dt. [Hide Solution] cosʻt + C 4

A:

Q: Evaluate the definite integral (За3 — 5а + 2) da fo 5а + 2) dx — a) Find an anti-derivative +C b)…

A:

Q: (a) Integrate the following function; i) SG) dx 1+9x² ii) S dx (b) Differentiate y = cosh-1(x² + 1)…

A: 5(a) (i) Given integral is ∫91+9x2dx ∫91+9x2dx=9∫1919+x2dx=∫119+x2dx=∫1132+x2dx Hence,…

Q: dx/(cos(x)-1) what is the answer to this integral? Use C for constant.

A: Use simple integration formula.

Q: Find the following definite integral where A is a constant and A > 2: | (10z + 17z +1) dx = %3D

A: We have to find the integral of∫2A(10x3+17x+1)dx, where A>2. Applying the sum rule of…

Q: Find the total differential du. 1. w = y tan a? – 2xy

A: To find the total derivative

Q: Use integration by parts to evaluate the integral: ∫sin(−12r)/e^2r

A:

Q: dx: Consider the indefinite integral e* +4

A: We have to evaluate the integration by substitution.

Q: |/ (cos(x) + sin(x))² dx

A: *Used the (a+b)2= a2 + 2ab + b2 formula.

Q: 3x 5cos(x)sin (r) dæ. Evaluate the definite integral

A:

Q: Q2 / Find dy/dx for the following functions; 1. y = Vtan(sin(x² – 1)) 2.((1+ cot x)³) dx 3. dx

A: Calculate derivative:  dydx=ddxtansinx2-13      =13tansinx2-12/3ddxtansinx2-1…

Q: dr Evaluate the integral / dx. sin x cos x

A:

Q: cos xdx (vii) S 5+sin2 x

A:

Q: 3x cosh a dx. 6. Calculate the definite integral, Jo -

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Q: Q5. (A) Evaluate [- dx +4x+3 (B) Use integration by part to evaluate ſe* sin (e** )dx

A:

Q: Find differential of the function ? = (x^2+2)^3 dy = ____ dx. When x = 4 and dx = 0.05, compute…

A: We will differentiate the function Y=(x^2+2)^3 as follows

Q: Q10/Evaluate the integral: sin(y) dy dx

A:

Q: b) f6xæ**dx 4 cosht)dt

A: We have to find the integrals.

Q: Find the most general antiderivative or indefinite integral. 2. cos 7x - csс"x) dx

A:

Q: Q2 / Find dy/dx for the following functions; 1. y = Vtan(sin(x² – 1)) 2. ((1+ cot x)3) d dx 3. d x2.…

A:

Q: Find the indefinite integral

A:

Q: ad the indicated integral (if it exists) E dz +1

A:

Q: to dx パー! 2 S dx 3J xtl to

A: (a) ∫2∞x2x3-1dx Solving the integral  Let  x3-1=t3x2 dx= dtx2 dx=dt3 Therefore, ∫2∞x2x3-1dx=∫7∞13…

Q: Find the antiderivative of the function f(x) = - 4 sin (4x) when C = 0. The antiderivative is

A:

Q: Incot3x dx sinh e* 1+9x

A:

Q: aluate the definite integral. x6 + a2 dx (a > 0)

A: We have to find the integral

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A:

Q: Evaluate the definite integral. "Tt/2 " d(sin x)? dx = (sin x)2 dx =

A:

Q: dy Find for the following functions dx x² + /siny – y² = 1

A: The objective is to find the derivative of the given function.

Q: (b) Find the following integrals: i. f(4x³+ sin x) dx. ii. ₁²(x²+)dx.

A:

Q: For ſ sin" (0) cos (0)d0, use a suitable change of variables to determine the indefinite integral.

A: Given : ∫sin7θcosθdθ