Trig and Integration help please?

Question

Trig and Integration help please?

Find, to one decimal place, the area bounded by $x = 0$ $x=0$ , $y = 0$ $y=0$ , $y = cos x$ $y=cosx$ and $y = {cos}^{- 1} x$ $y=cos^-1x$ .

Thanks!

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Answer 1 · 2017-10-04T14:31:55

$\int_{0}^{0.74} cos (x) d x + \int_{0.74}^{1} arccos (x) d x = 0.8$ $int_0^0.74 cos(x)d\x +int_0.74^1arccos(x)d\x = 0.8$

Explanation:

The plot of $cos (x)$ $cos(x)$ in purple and ${cos}^{- 1} (x)$ $cos^{-1}(x)$ in blue
enter image source here
The coordinate of intersection $(x, y) = (0.74, 0.74)$ $(x,y) = (0.74,0.74)$
So, between $(0, 0.74)$ $(0,0.74)$ , $cos (x)$ $cos(x)$ is the bounding function on the upper part, while between $(0.74, 1)$ $(0.74,1)$ , ${cos}^{- 1} (x)$ $cos^{-1}(x)$ is the bounding function.
Therefore the area of interest is:
$\int_{0}^{0.74} cos (x) d x + \int_{0.74}^{1} arccos (x) d x = 0.8$ $int_0^0.74 cos(x)d\x +int_0.74^1arccos(x)d\x = 0.8$

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Trig and Integration help please?

Find, to one decimal place, the area bounded by $x = 0$ $x=0$ , $y = 0$ $y=0$ , $y = cos x$ $y=cosx$ and $y = {cos}^{- 1} x$ $y=cos^-1x$ .

Thanks!

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

Trig and Integration help please?

Find, to one decimal place, the area bounded by x=0x=0, y=0y=0, y=cosxy=cosx and y=cos−1xy=cos^-1x. Thanks!

1 Answer

Explanation:

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Impact of this question

Find, to one decimal place, the area bounded by $x = 0$ $x=0$ , $y = 0$ $y=0$ , $y = cos x$ $y=cosx$ and $y = {cos}^{- 1} x$ $y=cos^-1x$ .

Thanks!