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Calculus 2 Assignment 5: Integration by Parts and Trigonometric Substitution - Prof. Tomor, Assignments of Calculus

Philippine Normal University (PNU)Calculus
Prof. Jimrey Tomoric

The fifth assignment for math 124 / math 29, calculus 2: integral calculus. Students are required to evaluate integrals using integration by parts or trigonometric substitution. Definite integrals should be solved first using properties/formulas and then by calculator. Ten integrals are provided for evaluation.

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2020/2021

Uploaded on 06/02/2021

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Prepared by: ENGR. JIMREY C. TOMORIC, REE, RME
MATH 124 / MATH 29
CALCULUS 2: Integral calculus
ASSIGNMENT NO.: 5
Name: ______________________________________ Course&Yr:______________ Score: ____________
General Instructions: Write your solutions in a long bond paper. A maximum of four (4) items per sheet.
Donโ€™t write at the back of each answer sheet.
Write your solutions/answers legibly and neatly.
Enclose final answer(s) in a box.
Evaluate the following integrals using INTEGRATION BY PARTS or TRIGONOMETRIC
SUBSTITUTION. For DEFINITE INTEGRALS, solve first by using the properties/formulas
then by calculator.
1. โˆซ๐‘ฅ4sin(2๐‘ฅ) ๐‘‘๐‘ฅ
2. โˆซ๐‘ฅ arccot ๐‘ฅ ๐‘‘๐‘ฅ
3. โˆซsec9๐‘ฅ๐‘‘๐‘ฅ
4. โˆซ๐‘ฅ3โˆš9 โˆ’ ๐‘ฅ2๐‘‘๐‘ฅ
5. โˆซ๐‘ฅ๐‘’๐‘ฅ๐‘‘๐‘ฅ
(1+๐‘ฅ)2
1
0
6. โˆซโˆš9โˆ’๐‘ฅ2๐‘‘๐‘ฅ
๐‘ฅ2
7. โˆซโˆš4โˆ’๐‘ฅ2
๐‘ฅ๐‘‘๐‘ฅ
8. โˆซ๐‘‘๐‘ง
(๐‘ง2+16)3/2
9. โˆซ๐‘Ÿ2๐‘‘๐‘Ÿ
โˆš๐‘Ÿ2โˆ’4
10. โˆซ(9 โˆ’ ๐‘ฅ2)5/2๐‘‘๐‘ฅ
3
0
Republic of the Philippines
EASTERN VISAYAS STATE UNIVERSITY
ORMOC CITY CAMPUS
ENGINEERING DEPARTMENT

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Download Calculus 2 Assignment 5: Integration by Parts and Trigonometric Substitution - Prof. Tomor and more Assignments Calculus in PDF only on Docsity!

Prepared by: ENGR. JIMREY C. TOMORIC, REE, RME

MATH 124 / MATH 29

CALCULUS 2: Integral calculus ASSIGNMENT NO.: 5 Name: ______________________________________ Course&Yr:______________ Score: ____________ General Instructions: Write your solutions in a long bond paper. A maximum of four (4) items per sheet. Donโ€™t write at the back of each answer sheet. Write your solutions/answers legibly and neatly. Enclose final answer(s) in a box. Evaluate the following integrals using INTEGRATION BY PARTS or TRIGONOMETRIC SUBSTITUTION. For DEFINITE INTEGRALS, solve first by using the properties/formulas then by calculator.

  1. โˆซ ๐‘ฅ 4 sin( 2 ๐‘ฅ) ๐‘‘๐‘ฅ
  2. (^) โˆซ ๐‘ฅ arccot ๐‘ฅ ๐‘‘๐‘ฅ
  3. (^) โˆซ sec 9 ๐‘ฅ ๐‘‘๐‘ฅ
  4. (^) โˆซ ๐‘ฅ 3 โˆš 9 โˆ’ ๐‘ฅ 2 ๐‘‘๐‘ฅ
  5. (^) โˆซ ๐‘ฅ๐‘’ ๐‘ฅ ๐‘‘๐‘ฅ ( 1 +๐‘ฅ)^2 1 0

โˆš 9 โˆ’๐‘ฅ^2 ๐‘‘๐‘ฅ ๐‘ฅ^2

  1. (^) โˆซ โˆš 4 โˆ’๐‘ฅ^2 ๐‘ฅ

๐‘‘๐‘ง (๐‘ง^2 + 16 )^3 /^2

  1. (^) โˆซ ๐‘Ÿ^2 ๐‘‘๐‘Ÿ โˆš๐‘Ÿ^2 โˆ’ 4
  2. (^) โˆซ ( 9 โˆ’ ๐‘ฅ 2 ) 5 / 2 ๐‘‘๐‘ฅ 3 0 Republic of the Philippines EASTERN VISAYAS STATE UNIVERSITY ORMOC CITY CAMPUS ENGINEERING DEPARTMENT