ENGR121 Assignment 7 Details
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Questions and Answers

Submit your assignment as a single pdf file named with your username. Your filename should end with ___

yourUserName.pdf

What is the integral of (5(2x))^4 dx?

Indefinite Integral required

What is the integral of 3e^(27x) dx?

Indefinite Integral required

What is the integral of 5 sinh(3x + 1) dx?

<p>Indefinite Integral required</p> Signup and view all the answers

What is the integral of sin(5t^2) dt?

<p>Indefinite Integral required</p> Signup and view all the answers

What is the integral of (14x^5 - 10x^3 - 2) dx?

<p>Indefinite Integral required</p> Signup and view all the answers

What is the integral of x/(e^x) dx?

<p>Indefinite Integral required</p> Signup and view all the answers

Given the values: ∫ from 0 to 20 of f(x)dx = 7, ∫ from 0 to 20 of f(x)dx = -3, and ∫ from 0 to 20 of g(x)dx = 5. What is the evaluation of ∫ from 13 to 20 of f(x)dx?

<p>Definite Integral required</p> Signup and view all the answers

What is the average value of f(x) = e^(3x) on the interval [1, 4]?

<p>Calculated using the formula for average of continuous functions</p> Signup and view all the answers

What is the r.m.s value of i(t) = 2 cos(4t) across the interval [0, π/2]?

<p>r.m.s value required</p> Signup and view all the answers

Study Notes

Assignment Overview

  • Assignment 7 is for the course ENGR121.
  • Due date is 11:59 PM on Wednesday, May 22, 2024.
  • Submission must be a single PDF file named with the user's username.

Submission Guidelines

  • Use exact forms for numbers; avoid decimal approximations.
  • For example, use symbols like π, e, and specific integers rather than their numerical representations.
  • Review submissions after upload to confirm accuracy.

Indefinite Integrals

  • Tasks include finding indefinite integrals for functions such as:
    • (a) ( \int (5(2x)^4) , dx )
    • (b) ( \int 3x^{4/16} , dx )
    • (c) ( \int 3e^{27x} , dx )
  • Other integrals include:
    • (d) ( \int (14x^5 - 10x^3 - 2) , dx )
    • (e) ( \int 5 \sinh(3x + 1) , dx )
    • (f) ( \int \sin(5t^2) , dt )

Definite Integrals with Given Values

  • Given values include ( \int_0^7 f(x) , dx = 7 ), ( \int_0^{20} f(x) , dx = -3 ), and ( \int_0^{20} g(x) , dx = 5 ).
  • Evaluate:
    • (a) ( \int_{13}^{20} f(x) , dx )
    • (b) ( \int_0^{20} 7g(x) , dx )
    • (c) ( \int_0^{20} (2g(x) - 3f(x)) , dx )
    • (d) ( \int_{13}^{20} 4f(x) , dx )

Additional Definite Integrals

  • Tasks include evaluating:
    • (a) ( \int_0^7 \ln(6) , dx )
    • (b) ( \int_0^{\pi} \sin(6x + 3) , dx )
    • (c) ( \int_0^4 6(3t)^4 , dt )
  • Also includes more complex integrals:
    • (d) ( -2 \int_0^{\pi} (4e^{-7x} + e^4) , dx )
    • (e) ( \int_0^1 (4x^4 - 3x^3 + 5x - 7) , dx )
    • (f) ( -\pi \int_0^{\pi} |\sin(x)| , dx )

Improper Integrals

  • Tasks involve evaluating improper integrals:
    • (a) ( \int_{-\infty}^0 x e^x , dx )
    • (b) ( \int_{-10}^{10} \frac{1}{x + 3} , dx )

Integration by Substitution

  • Perform substitution to solve:
    • (a) ( \int_0^1 5x^{2/3}(x + 7) , dx )
    • (b) ( \int \cos(\ln(7x) + 3) , dx )
  • Further tasks include integration of:
    • (c) ( \int e^{-4 \sin(x)} , dx )
    • (d) ( \int \frac{3}{2x^4 + 3} , dx )
    • (e) ( \int x(4x + 7)^6 , dx )

Average and RMS Values

  • Calculate the average value of ( f(x) = e^{3x} ) over the interval [1, 4].
  • Determine the root mean square (RMS) value of ( i(t) = 2 \cos(4t) ) across the interval [0, ( \frac{\pi}{2} )].

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Related Documents

ENGR121 Assignment 7 PDF 2024

Description

This document outlines the requirements for ENGR121 Assignment 7 due on May 22, 2024. It emphasizes the need for submissions to be in a single PDF format and to maintain exact numeric forms for mathematical constants. Follow the guidelines to ensure a successful submission.

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