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negative exponent 1/(7^3)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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∫₃⁵4x2−8x² dx

Solution

14 ln(3599 )

Decimal

−0.25994…

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Solution steps

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∫₃⁵4x2−8x² dx

Đưa hằng số ra ngoài: ∫a·f(x)dx=a·∫f(x)dx

=4· ∫₃⁵x2−8x² dx

Áp dụng Phép đổi biến tích phân: ∫₋₇₀⁻¹⁹⁸−116u du

=4· ∫₋₇₀⁻¹⁹⁸−116u du

∫_a^bf(x)dx=−∫_b^af(x)dx, a<b

=4(−∫₋₁₉₈⁻⁷⁰−116u du)

Đưa hằng số ra ngoài: ∫a·f(x)dx=a·∫f(x)dx

=4(−(−116 · ∫₋₁₉₈⁻⁷⁰1u du))

Sử dụng tích phân chung: ∫ 1u du=ln(|u|)

=4(−(−116 [ln|u|]₋₁₉₈⁻⁷⁰))

Rút gọn 4(−(−116 [ln|u|]₋₁₉₈⁻⁷⁰)): 14 [ln|u|]₋₁₉₈⁻⁷⁰

=14 [ln|u|]₋₁₉₈⁻⁷⁰

Tính toán các giới hạn: ln(70)−ln(198)

=14 (ln(70)−ln(198))

Rút gọn

=14 ln(3599 )

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

negative exponent 1/(7^3)

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