Question

Math

Posted 2 months ago

```
Graph $y=2 \cos \left(\frac{1}{2} x\right)-1$ in the interactive widget.
Note that one moveable point always defines an extremum point in the graph and the other point always defines a neighbouring intersection with the midline.
```

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Answer from Sia

Posted 2 months ago

Solution by Steps

step 1

To evaluate the definite integral, we use the given function under the square root

step 2

The function to integrate is $\sqrt{16 e^{-2 t} + \sin^2(1 + \sqrt{t})}$

step 3

We integrate the function from $t=1$ to $t=3$

step 4

The result of the integration is approximately $1.8606$

1 Answer

The integral of the given function from $t=1$ to $t=3$ is approximately $1.8606$.

Key Concept

Definite Integration of Functions

Explanation

The definite integral of a function gives the area under the curve of the function between two points on the x-axis. In this case, the function is a combination of an exponential decay and a squared sine function, integrated from $t=1$ to $t=3$.

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