Direction: Find the integral of the following functions: 1. S(5 cos x + 7 sin x) dx 2. S(3tan2 x+3)dx 3. S(4x – csc? x)dx

Q: Evaluate the definite integral: 4 dx 0 x2+16

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Q: What change of variables is suggested by an integral containing * Vx² – 4? O a cosø O none of the…

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Q: 2x4 +3x2 – 1 Rewrite dx as integral of sum of partial fractions. (x³ – 4x² + 5x)? - B + E |dx x+1'…

A: we can reduce into partial fraction

Q: x³ + 6x² + x+2 s ax + In[cx + 1}*(x² – x + 1)°| + fx-1 Tan-1. V3 The resulting integral of x³ +1 +…

A: use simple integration formula.

Q: Vx In 2x dx=u v- v-fvdu Using Integration By Parts, Find Uv- du O 3 xVx In 23 2 12x- dx | O 2 Xx In…

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Q: 5. sin (2x) dx

A: To evaluate: ∫sin22xdx ⇒I=∫sin22xdx We know that 1-cos2x = 2sin2x

Q: (x Using a suitable trigonometric substitution, the resulting integral in terms of V9x²+4 Consider e…

A: Given problem:-

Q: Consider the following. (If an answer does not exist, enter DNE.) (x) = x6e=x (a) Find the…

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Q: Use the properties of infinite series and the fact that Σ 1 1. 1 and 4 5" n = 1 6' n = 1 5 to find…

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Q: 1. Evaluate the following limits. 4x – 7 3x2 – 2r – 5 1 c. lim I-1- |I + ¤|

A: We put the limit .

Q: In polar coordinate system, which of the following does not refer to the point (3, pi/6)?    A. (3,…

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Q: +00 dx -Evaluate the improper integral x (In x)²

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Q: JV-x² + 4x+5 Consider dx. Using trigonometric substitution, what is the integral form in terms of 0?

A: We have to determine  integral form of given question

Q: 2n+1 5. Σ 'n°(n+1)² n=1

A: let  bn=1n3∑n=1∞1n3    is convergent   by p series  Recall ∑n=1∞1nP    is convergent  iff p>1

Q: sin(3x)cos(3x) sin(2x) 의[cos(2x)-1]+ +C 12 8 4

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Q: Consider the following function. f(x) = 2x3 - 12x² + 18x – 7 Find the derivative. f'(x) = Find any…

A: The given function is: f(x)=2x3-12x2+18x-7

Q: 2x+11 3. 1 dx, evaluate Consider 3 x² + x – 6 = xp dx X+3 X- 2 X+3 X-2 |(x- 2)° +C In x+3 x-2 In +C…

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Q: A clothing manufacturer has the marginal profit function MP(x) = 40 - 0.02x, Os xs 100 (in dollars…

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Q: Q2/ solve the Differential Equation [ (2xy+3y²)dx = (x² + 2xy)dy ]

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Q: Find the centroid of the region R bounded by the graphs of y x and y 1. 1) Which of the following…

A: To find the area of the region R.

Q: 16. Follow (and show proof) of each step below to estimate the area under the curve f(x) = 3 cos x…

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Q: How can you relate antiderivatives as an opposite of derivatives in your life? explain

A: Solution is given below:

Q: (Ca' - x*

A: we know that,           integration of xn dx = xn+1n+1.  and x-y2= x2+y2-2xy

Q: 1. Prove the following limit. a) f(x)=x²+2x+6 where lim, 3 f (x)=21 x→3 b) limx? -x+1=-5 c) lim x→2…

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Q: You’ve started a small business selling handmade keychains. You’ve given one frequent customer the…

A: Here, the given function for the price is: p(x)=10-x2

Q: ind the area and the circumference of a circle with diameter 6 m. Ise the value 3.14 for a, and do…

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Q: x² –9 dx Given: r3

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Q: s2+3 1. (s-3)(s+5)(s-1)² s2-s+3 s3(s+5)(s-2) s-8 (s-3)(s²+2s+17) (s+1)²(s²–4s+85) s² +5s-2…

A: let's solve option (2) L-1 s2-s+3s3s+5s-2 By partial fraction, s2-s+3s3s+5s-2=As+Bs2+Cs3+Ds-2+Es+5…

Q: Find all points (x,y) on the graph of y = x-4 with tangent lines perpendicular to the line y = 4x +…

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Q: 2 Evaluate V4-x² dy dx using polar 2x-x2 Coordinates.

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Q: (a) How many integers from 200 to 2000 inclusive are multiples of 4?  (b) How many integers from…

A: As per our guidelines we are supposed to answer only three sub parts of the question. So I am…

Q: dx ex sin2 (e

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Q: ay Do not simplify your answers. de 3. Solve for sec(3r2 + In 2) eVI+2 +9 - log(2³ + y) C. r Cos y =…

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Q: Integration by Parts In this case you will often be successful if you take u to be the function…

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Q: 2- oiffemontiake with nespeef fo z and ataking X as a cams fant. he * (2-2a)" y.l00 (2-2x)" (1-0) =…

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Q: If R is the region enclosed by x-axis, y = -3x and x = -2, then evaluate the following double…

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Q: A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No…

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Q: 5. Let f be a function satisfying the following properties: continuous on R \ {0} • f(-1) = -3 •…

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Q: Consider -(x Using a suitable trigonometric substitution, the resulting integral in terms of 0 is…

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Q: g(b) Use the Substitution Formula, f(g(x)) g'(x) dx = | f(u) du where g(x) =u, to evaluate the…

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Q: |sin(x)cos(2x)sin(3x) dx sin(3x)cos(3x), sin(2x)cos(2x) sin(2x) 12 8 8. + C 4 sin(6x) sin(2x),…

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Q: Find the average rate of change of the function over the given interval. R(0) = 40 +1; [6,12] AR…

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Q: Find the general (real-valued) solution of the following differential equations. If an initial…

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Q: s2x²-x²+ x+2 A dx find A + B+C+D• X +1 Consider dx = x4 + x3 3. 2 4 O O o o

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Q: 4. A father is running west at 5 m/hr and his son is running north at 6 m/hr. Both are headed for…

A: I am attaching image so that you understand each and every step.

Q: V4-x2 aluate dy dx using pol 2x-x2 prdinates.

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Q: Let C be a curve that is defined by x = 4 sint and y = cos t, t e [0, 27]. Determine (a) the time…

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Q: Find the arc length of the parametric curve. x = e', y = e, z = v2t; 0<t < 6 V2t; 0<t<6 x = L =

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Q: in how many distnct ways can the letters of the word DEEDS be arranged? Oways (Type a whole number)

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Q: If you are going to evaluate the integral f dx using trigonometric substitution, the answer is 2(tan…

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