Determine tne arca of thc region outside of r=2 and inside of r- 3+ 2si no .

Q: 10. Prove by using integration by change in variable the ff. integral: dx :du 3D arcsecх+ С xVx2 – 1

A: We have given the integral ∫dxxx2-1 = I(say)     Put   x2-1 = t   ⇒x2= t2+1     Differentiate w.r.t…

Q: Evaluate iterated integral.

A: Given, ∫12∫121xdx dx

Q: Evaluate the integral. er HEAD ² y³ In(x) dx, y> 0 ind

A:

Q: Evaluate the integral (2x+3y) dx + (6x – y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

A: To Evaluate: I=∫C(2x+3y)dx+(6x-y)dy along the parabolic arc y=x2 from (0,0) to (1,1).

Q: Use a double integral to find the area of the shaded region.

A: The formula for the area of a region of a polar curve, r(θ) bounded by θ=a to θ=b in the polar…

Q: Choose among the following suitable to define the given S(e + +) arctan{ dx O By parts, the red part…

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

Q: x arcsin(x²) dx;

A: Given that: *∫sin-1u×du=u×sin-1u+1-u2+C The given expression is, ∫x×sin-1x2×dx Let,  x2=u,…

Q: Evaluate the double integral sin(y' +1)dydx.

A: Use the change of order of integration to solve this problem.

Q: sketch the described regions of integration.0 ≤ y ≤ 1, 0 ≤ x ≤ sin-1 y

A: Given: 0≤y≤1 0≤x≤sin-1y

Q: Find the area of the region that lies inside both curves

A:

Q: Use double integrals to find the area inside the curve r = 5sin(e)

A: The given curve is:

Q: Sketch the region of integration. 1. dx dy 1 +>

A:

Q: Evaluate the integral. arctan dx 1

A: For evaluating the given integral, we will use the concepts of integral by parts and integration…

Q: Evaluate the integral arc y = x² from (0,0) to (1,1). NOTE: Enter the exact answer. (2x + 18y)dx +…

A: Given integral is ∫C(2x+18y)dx +(3x-y)dy We have to evaluate given integral along a parabolic arc…

Q: Calculate the integral (а) dx (*/3 Vtan 0 (b) п/4 -do sin 20

A: Given : (a)  ∫-∞∞x5e-x2 dx    (b) ∫π4π3tanθsin2θdθ

Q: etch the region of integration. (Select the correct graph.) In 5 5 [ins T3 124 af In y dy dx

A: Given the function ∫0ln(5)∫ex5 1ln(y) dy dx. The objective is to sketch the region of integration…

Q: 3. Evaluate the improper integral: dx | Tale + 1)'

A:

Q: 6. Set up integrals to compute the arc lengths of the curves y = r², y = 26, y = x¹⁰ defined for z…

A: Let's find arc length of given curves on interval [0,1].

Q: 10. Prove by using integration by change in variable the ff. integral: dx du = arcsec x + C xVx2 - 1

A: To show∫dxxx2-1=sec-1x+C.

Q: SSy'e»-'dy

A:

Q: Evaluate the integral / (2x + 6y)dx + (15x – y)dy a C arc y = x² from (0,0) to (1, 1). NOTE: Enter…

A:

Q: Find the integral of (x)(arctan x) dx,

A: Given: evaluate

Q: Find the approximation of the integral. 1= [e*dx Using Romberg's rule derived from Trapezoidal rule…

A: Given integral I=∫01e-x2dx Here we use Romberg's rule derived from Trapezoidal rule for 1,2,4,8…

Q: Evaluate the double integral: dy dr

A:

Q: Sketch the region of integration. Then evaluate the iterated integral sin(x²) dx dy.

A:

Q: evaluate the intregral of cos2xesin2x dx

A: topic - indefinite integral

Q: Evaluate the iterated double integral: esec y+1 dy dx. VE sin y sec

A: To evaluate the iterated double integral :               ∫14∫sec-1xπ3  esecy+1sin ydydx

Q: TX Evaluate the integral dx dy by reversing the order of integration. 2 Cos 0.

A:

Q: Ssin (3x)cos (3x) dx 3. Evaluate the trigonometric integral ·

A:

Q: Set up an integral that represents the arc length of the curve y 2xi from the point (0, 0) to (2,…

A: our objective is to setup the arc length formula

Q: Compute the indefinate integral. integral (1-sin^2(x))/cosx * dx

A: Consider the given integral.

Q: Evaluate the integral. arctan(5t) dt

A: Here we evaluate the integral∫ arc tan 5t dt

Q: Which integral computes arc length of f(x) = x5/2 on [0, 1]? 1 49 -x' dx 1+ 4 - 1 | V1+ x° dx 1 1+…

A: We have to find the arc length

Q: Use double integrals to find the area inside the curve  r = 3 + sin(θ).

A: Find the area enclosed by the curve r = 3+sin θ , using double integration method.

Q: Evaluate the iterated integral. (2х — 4у) dy dx Exact number, no tolerance. (2x – 4y) dy dx = i -1

A: The given integral is: I=∫111∫-11(2x-4y) dy dx

Q: integral arctan4t dt

A:

Q: Evaluate the integral dx using Weddle's rule. o e-1

A:

Q: Evaluate the integral. ∫arctan 4t dt

A:

Q: y = sin(x), y = 2x

A:

Q: 5. Find the area enclosed by the inner loop of the curve r = 1-3 sin 0

A: Area Between Functions With Integration: The interval of the inner loop of the given polar curve is…

Q: Find the arc length of f(x) = e² from x = 0 to x = 1. Be sure to recall integration techniques we…

A: In the given question we have to find the arc length of the curve from x=0 to x=1. Concept: The…

Q: Set up an integral to find the arclength of the curve y = ln(x) over the interval [1,5]. Use an…

A: To set up the integral for arc length (S), use the formula for arc length:…

Q: Compute the defined integral So [1+ e* sin(4x)] dx using the trapezoidal method with two segments.…

A:

Q: I+tgX dx; 2 COS X cos

A: Given: ∫1+tanxcos2xdx

Q: Calculate the area between the curves r2 16 sin 20 and p2 16 cos 20 .Show by drawing. %3D %3D

A: We will draw region first, then find the area using double integral

Q: Evaluate wing Integration by Tangorometre bodetrdadin 1.S Jas-x? dx

A: Solution

Q: The area of the surface generated by rotating the curve y = 1 = cos(3x), where 0 ≤ x ≤ , about the…

A: Let's find Area of surface,when rotated about x axis.

Q: isolated singular point 1. z/((z^3)+z) 2. exp(tan(1/z)) 3. (1/(z^2)) * exp(1/(z^2)) z=4 is apole of…

A:

Q: Jy Find the area of the inner loop of the curve r = 9 cos 0 - 4 by using double integral.

A:

Q: 5. Use integration to find the exact area outside r = 4 cos 0 and r = 4 sin 0 but inside r = 2.

A: