Approximate the following integral using both Trapezoidal Rule and Simpson's Rule with n = 4: Trapezoidal Rule: Simpson's Rule: Use exact answers, not rounded values! $3 √z +1dz

Q: Use (a) the Trapezoidal Rule integral 1to 4    sqrt x cos x dx                 with n= 8

A: The trapezoidal rule is the technique used to find the approximation of the integral by dividing the…

Q: What integral gives the length of a semicircle of radius 3?

A: •The integral       L=∫−33​9−x2​3​dxgiven the length of the given semicircle of radius 3.• The…

Q: 1 Evaluate the integral S√I+2x f dx

A: We have definite integral  Substitute 1+2x=z2  to make integration radical free as I have done…

Q: let b be a constant. use definition to find  (integral 0 to b)(x+1)^2 dx.

A: Given: The expression of integral as ∫0bx+12dx, where b is a constant, To evaluate: The value of…

Q: Q.3 Find the value of x, for which the geometric n series Σ(3) (x + 4)" converges.

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple subpart…

Q: (B) Evaluate the integral ( Use Trigonometric Substitutions ) 25 x2 dx

A: We use Trigonometry substitution to solve this integration

Q: 5 3) S-²³2 235-1 dx a) Briefly explain why this integral is improper.

A: Follow the procedure given below.

Q: use the u substitution to evaluate the integrals  definite integral 7 at the top and 0 at the bottom…

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Q: Use Gauss-Legendre formula to evaluate the integral e¯x*dx_with n = 3.

A: Evaluate the integral          ∫01ex2dx using Gauss-Legendre formula with n=3.

Q: can you also use the trapezoid rule with N=4 to approximate the integral?

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Q: Use geometry and properties of integrals to evaluate

A: Given integral is ∫15 x-2+-x2+6x-5dx. The above integral can be written as below. ∫15…

Q: When computing a contour integral, are you able to split the function into two parts and add the…

A: Solution: Contour integral.

Q: Evaluate the integral √(4 by making the appropriate substitution: u √ (432² dx [ X (4x² + 11) 7 = X…

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Q: Use geometry and properties of integrals to evaluate the followingdefinite integrals.

A: Given

Q: Evaluate the given integral using Trigonometric Substitution 27e#dæ (6e# –9e2z +10)

A: Given integration is                                     ∫27 e4xdx6ex-9e2x+10 The formula for…

Q: Use the Midpoint Rule with n = 4 to approximate the integral 10 I Va + 11 da = Round your final…

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Q: evaluate integral by using techniques I=∫ x²sin⁴xdx

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Q: Use Simpson's rule with 4 strips to approximate f₁² √1 + x² dx

A: The given integral ∫121+x2dx. We have to find the value of the integral using the Simpson's rule…

Q: Use geometry and properties of integrals to evaluate

A: we have to  integrate the given integral ∫01(2x+1-x2+1)dx

Q: Use the trapezoidal rule with five intervals to evaluate the integral i √√√-1da, correct to four…

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