Mathematics: Evalute the integral (sin^3 (x)/cosx)dx

Evalute the integral (sin^3 (x)/cosx)dx

Ответ:

jessicajose4238

08.01.2022

$\int { \frac{sin ^{3} x}{cos x} } \, dx= \\ = \int { \frac{sin ^{2} x*sin x}{cos x} x} \, dx= \\ = \int { \frac{(1-sin ^{2} x)*sinx}{cos x} } \, dx =$
t = cos x,
dt = - sin x dx;
$= \int { \frac{-(1- t^{2}) }{t} } \, dt= \\ = \int { \frac{t ^{2}-1 }{t} } \, dt = \\ =\int {t} \, dt - \int { \frac{1}{t} } \, dt = t^{2}- ln t = \\ = \frac{cos ^{2} x}{2}-ln ( cos x ) + C$

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Ответ:

vbucks72

07.03.2020

Mathematics

615.8 m³

Step-by-step explanation:

The formula for the volume of a cone is ...

V = (1/3)πr²h

For your given radius and height, the volume is ...

V = (1/3)π(14 m)²(3 m) = 196π m³

V ≈ 615.75216 m³ ≈ 615.8 m³

The π button on the calculator uses a value slightly larger than 3.14, so an answer with 3.14 for pi will be incorrect.

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Evalute the integral (sin^3 (x)/cosx)dx

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