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achse y=25-x^2

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bereich 7x²+6+2x²−4

Solution

f(x)≥ 2

Interval Notation

[2, ∞ )

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Solution steps

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∫ cos⁵(x)dx

Umschreiben mit Hilfe von Trigonometrie-Identitäten

=∫ (1−sin²(x))²cos(x)dx

Wende U-Substitution an: ∫ (1−u²)²du

=∫ (1−u²)²du

Multipliziere aus (1−u²)²: 1−2u²+u⁴

=∫ 1−2u²+u⁴du

Wende die Summenregel an: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx

=∫ 1du−∫ 2u²du+∫ u⁴du

∫ 1du=u

∫ 2u²du=2u³3

∫ u⁴du=u⁵5

=u−2u³3 +u⁵5

Setze in u=sin(x) ein

=sin(x)−2sin³(x)3 +sin⁵(x)5

Füge eine Konstante zur Lösung hinzu

=sin(x)−2sin³(x)3 +sin⁵(x)5 +C

Solve instead

domäne 7x²+6+2x²−4

scheitelpunkte 7x²+6+2x²−4

invers 7x²+6+2x²−4

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

achse y=25-x^2

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