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Integral Cal

The document contains a series of integral calculus problems and their solutions. Each problem involves finding the integral of a function, with detailed steps leading to the final answer. The solutions include constants of integration and various mathematical transformations.

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luvellemagalona03
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8 views2 pages

Integral Cal

The document contains a series of integral calculus problems and their solutions. Each problem involves finding the integral of a function, with detailed steps leading to the final answer. The solutions include constants of integration and various mathematical transformations.

Uploaded by

luvellemagalona03
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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NAME: Luvelle Neprethy O.

Magalona

YEAR & SECTION: AB-ECON 2A

1. ∫√x(x + 1/x) dx

∫(x³/² + x⁻¹/²) dx

x⁵/² / (5/2) + x¹/² / (1/2) + C

= (2/5)x⁵/² + 2x¹/² + C

2. ∫(5t² + 7)/t³/⁴ dt

∫(5t⁵/⁴ + 7t⁻³/⁴) dt

5(4/9)t⁹/⁴ + 7(4)t¹/⁴ + C

= (20/9)t⁹/⁴ + 28t¹/⁴ + C

3. ∫(6x⁵ - 3x⁴ + 4x³ - 9x² - x + 7) dx

x⁶/6 – (3/5)x⁵ + x⁴ - 3x³ - x²/2 + 7x + C

= x⁶ - (3/5)x⁵ + x⁴ - 3x³ - (1/2)x² + 7x + C

4. ∫(5 csc²x – 3 sin x) dx

5(-cot x) – 3(-cos x) + C

= -5 cot x + 3 cos x + C

5. ∫(cot²x + sec²x – 8) dx

∫(csc²x – 1 + sec²x – 8) dx

∫(csc²x + sec²x – 9) dx

-cot x + tan x – 9x + C

= -cot x + tan x – 9x + C

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