Q1/ Evaluate I'(1/2)

Q: Use integration by parts to find the indefinite integral.

A: To find the indefinite integral I =∫xsec2x dx By using integration by parts, ∫fg'=fg-∫f'gf = x ,…

Q: A coat of paint of thickness 0.02 cm is to be applied uniformly to the faces of a cube of edge 21…

A: We know that,

Q: Use differentials to approximate the value of 52.1. 100+ 5ln5 50+ 6ln5 50+ 5ln5 2 100+ 6ln5 4

A:

Q: 3) f(x) = (x + 4) Standard form: Y-int:

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: integral by part x² dx

A: Given that  The integral is

Q: Evaluate ∫x3 √(1 - x2) dx using integration by parts.

A: Consider the given integral Here the objective is to evaluate given indefinite integral.

Q: A coat of paint of thickness 0.03 cm is to be applied uniformly to the faces of a cube of edge 29…

A: Let the side length of the cube be S = 29.Side increase on each side = 0.03 cm.Total increase in…

Q: find derivatines of the first derivatives indol and Zuotients.. y= tanx %3D

A: Given function is y=extan−1x Use formula ddxex=ex and ddxtan−1x=11+x2 Differentiate y=extan−1x with…

Q: Using Differentials, approximate (4499)2-(401)2 AM

A: To approximate: 4.9992-4.012 Let, z=fx,y=x2-y2x0=5, y0=4 For the function z=f(x, y) at the point…

Q: Find the theoretical error bound in approximating SN" sin(x?) dx using Boole's Rule.

A: The theoretical error bound in approximating the integral∫0πsinx2dx using Boole's rule is shown…

Q: tion of all components of v(3) correct to two decimal places.

A:

Q: Find definite integral.

A: The given integral can be solved by the method of substitution. The substitution that will be used…

Q: Before integrating, how would you rewrite the integrand of S(x* + 2)² dx?

A: To solve: ∫(x4+2)2dx

Q: Jse differentials to approximate 47. (Express as a rational number.)

A:

Q: x' V4-x dx

A:

Q: d arctan (tanh x) dx Show that sech 2.x.

A:

Q: S(歳)dx 2

A:

Q: ach to solve omogeneous ential equatior

A: Given - The differential equation To find - Use the superposition approach to solve the given…

Q: Verify the power rule for integration fx'dx= n+1

A: Given a power rule of integration,

Q: Finel for r=1-Sino

A:

Q: Find indefinite integral.

A: Let the given integral be y - y = ∫x12+3x-23 dx      Identity to be used - ∫xndx = xn+1n+1+C

Q: (Use Simpson's Rule with n=4 to approximate 5x* dx

A:

Q: Verify Eq. (2): cosh 2 x - sinh2 x = l.

A:

Q: Original Integral Vx dx x xp,

A: Given function is x4

Q: Use Simpson's Rule with n = 4 to approximate 5x* dx.

A: The solution is given as

Q: Compute. integral (1) / (square root 1 + x2)3 dx

A:

Q: Use differentials to approximate the value of <2.1.

A: Given  Find the value of 52.1

Q: complete solution

A:

Q: Find integral.

A:

Q: Find the total differential. z = 10x8y6 dz =

A: GIVEN: z = 10x8y6

Q: 3 tanh (In(4x)) sech" (In(4x)), I) y = tanh (In(4.x)) [y

A:

Q: What is the value of integral /tanx dx ?

A:

Q: 3 dx V16-x²

A:

Q: Find y' by ased proportici Ln Xャ3

A: Taking natural log both side

Q: Use differentials to approximate the value of (2.001)’.

A:

Q: Use differentials to approximate √16.5.

A: Given:

Q: Evaluate integral x^2e^-x^3 dx

A:

Q: ary differentia att=0 the ing

A:

Q: Match the graph with the first order differential

A: In this question we will use basic concepts of calculus i.e graphing of differential equation.…

Q: Find the indefinite integral ∫ x2 sech2 x3 dx

A: We have to find indefinite intrgral  ∫x2sech2x3dx We have ∫x2sech2x3dx  Take x3=t⇒3x2dx=dt⇒x2dx=13dt…

Q: 1. cosh (j) 2. tanh 3. 3. In(2 + j3)

A:

Q: Uje differential to estimate V32.02 correct to 4 decimai places.

A: Given : 5√(32.02)

Q: 4. Evaluate x sin2x dx Integration by parts

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Integral of sec^4(3x) dx

A: Given ∫sec4(3x)dx

Q: Use Simpson's Rule with n = 4 steps to estimate the integral. 5) dx

A:

Q: Use integration by parts to find the indefinite integral ∫x sec2 x dx

A: Given: ∫x sec2 x dx

Q: Q3: Find 1. cosh(5x)+ sinh(5x) 2. (sinhx+ coshx)*

A: Given,

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.