Determine the integral of the ff. functions. 1. S - 10 sin 5x dx 2. S 4 x cos x² dx 3. S sec 2 (3x + 7) dx 4. S (x+2) csc 2 (x² + 4x - 11) dx 5. S 12 csc (-6x) cot (-6x) dx 6. ( 2 x3 cot x4 dx

Q: Evaluate the integral. dx (x – 4)(x – 7) - (Use symbolic notation and fractions where needed. Use C…

A: Solving the problem by finding the value of integral.

Q: If f(2) = 10, f' is continuous, and f'(x) dx = 20, what is the value of f(3)? f(3) =

A:

Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is…

A:

Q: 13. Solve the following system of equations using either the substitution method or the graphing…

A: Linear equation: Linear equations are first-order equations. An equation with a homogeneous variable…

Q: Find the partial derivative. = (a² + 4x – 2y)° - dz II

A:

Q: x³dx is equivalent to Using trigonometric substitution, Vx² –4 A 6/ tan*0 seco do B) None © 8 sec0…

A:

Q: Find the equation of the tangent line to the curve at the point (5,3) given that x2+xy+2y2=58

A:

Q: Lef foo) the Gempesition (foj)G) 2001 2nd gG6) = e²7#Defermine

A:

Q: The particular solution that satisfies the differential equation and the initial condition of dy/dx…

A: Given , dy/dx = x2+2x-4 We can get y by integrating.

Q: Solve the logarithmic equation algebraically. Approximate the result to three decimal places. (If…

A:

Q: 4.Graph one cycle of function given below. State domain, range, period, phase shift, vertical shift…

A:

Q: Find V · (F × G), if F(x, y, z) = 3ri+j+6yk and G(x, y, z) = xi+ yj – zk. V· (F × G) ||

A:

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution . 1.

A:

Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve).…

A:

Q: Solve for x. (Round your answer to three decimal places.) ex 8. %3D X =

A: We can solve by taking natural log both side and solve, so I'm providing hand written solution for…

Q: One of the correct steps to evaluate x2inx x²Inx dx to yield the correct integral A x?Inx B 1 x3 dx…

A:

Q: Write a definite integral for the area of the region bounded by y = 2 - x² and y = x2. Do not…

A:

Q: Find the value of n in the following definite integral. So 4x° dx 1 Answer:

A:

Q: du u and dx du Identify u and dx du u" dx Finding for the integral dx.

A:

Q: a) Find the average acceleration in the first 3 seconds. b) The particle changes direction twice.…

A: Here I am providing my handwritten solution.

Q: The rate of decay of radium is proportional to the amount present at any time. The half-life of…

A: The understanding of radioactive decay is required. The explanation part is given below.

Q: 5. A ladder of length 4v3 metres is resting on a wall. The wall makes a 60-degree angle with the…

A:

Q: Identify u and dv for finding the integral using integration by parts. Do not integrate. In(5x) dx u…

A: We will evaluate the given integral as shown below

Q: The differential equation (xy2 + y)dy = (x+1)dx is separable. %3D

A:

Q: Evaluate: /x*V1-x*dx A None 3 글(1-x4) 2 +C В 3 -(1-*) C 3 (D (1-x+) +c 3 1(1-x*) ? +E E

A:

Q: csc?y dy is equal to A -у соty — coty dy B) None у сoty — coty dy D у сoty + coty dy

A:

Q: 1. Find the volume of the solid obtained by rotating the region bounded by the given curves about…

A:

Q: 3. Graph the function f(x) = 1 and estimate the area for -2 <x < 2 1+ x2

A:

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: Given

Q: . .............. Solve the exponential equation algebraically. Approximate the result to three…

A:

Q: Use logarithmic differentiation to evaluate f'(x). (x + 4)8 f(x) = (3x - 3) f'(x) =|

A:

Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: Given: f(t)=-16t2+444t+8

Q: Find the work done by the force field F in moving an object from P(-9, 7) to Q(3, 3). 2.x. F (r, y)…

A:

Q: Write an equation for the ellipse that has vertices (+7, 0) and co-vertices (0, ±6). Provide your…

A:

Q: The particular solution that satisfies the differential equation and the initial condition of dy/dx…

A:

Q: - 3 Let f(x) = 8xVæ + x2. f'(x) =

A: Use the derivative for finding the answer.

Q: ng one unit of the product for one year, f be the fixed setup cost to manufacture the product, g be…

A: Given :

Q: 3x? (x³ + 4)* dæ = 5120 Select one: O True O False

A:

Q: The widths (in meters) of a kidney-shaped swimming pool were measured at 3-meter intervals as…

A:

Q: A ladder of length 4/3 metres is resting on a wall. The wall makes a 60-degree angle with the…

A:

Q: The particular solution that satisfies the differential equation and the initial condition dy/dx =…

A: topic- differential equations

Q: Find the standard form of the equation of the ellipse with the given characteristics.

A:

Q: Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x² + y = 9 and…

A:

Q: QUESTION 4 At an awards ceremony, 6 women and 4 men are each to receive an award and are to be…

A:

Q: Find the arc length L of the graph of r(t). r() = r° i + 1 j+Vor k, 3 <t<7 L = i

A: Given problem:-

Q: 81 fx, y) dy dx 10 10 O-10 10 1아 1아 -10 10 -10 -10 81 -x F(x, y) dy dx = f(x, y) dx dy

A: we have to change the limit of integration.

Q: Compute the surface area of the cone generated by revolving c(t) = (t², t) for 0 <t < 6. (Use…

A:

Q: 14) Find aset of parametnic equetians for the rectangular aquetiag d= 4x2 tust Setisfies fue…

A:

Q: Use only the fact that 3x(2 - x)dx = 4 and the properties of integrals to evaluate the integrals in…

A:

Q: We have a piece of cardboard that is 14 inches by 10 inches and we're going to cut out the corners…

A: We need to determine height of the box.