Rob is saving to buy a new MP3 player. For every $16 he earns babysitting, he saves $9. On Saturday, Rob earned $96 babysitting.
2 answers:
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Split up the integration interval into 4 subintervals:
The left and right endpoints of the -th subinterval, respectively, are
for , and the respective midpoints are
- Trapezoidal rule
We approximate the (signed) area under the curve over each subinterval by
so that
- Midpoint rule
We approximate the area for each subinterval by
so that
- Simpson's rule
We first interpolate the integrand over each subinterval by a quadratic polynomial , where
so that
It so happens that the integral of reduces nicely to the form you're probably more familiar with,
Then the integral is approximately
Compare these to the actual value of the integral, 3. I've included plots of the approximations below.
True
Note that:
The graph of sine and cosine functions are very similar. They only have a shift in the x -axis.
That is, sin x = cos (90 - x)
Since there is a great similarity between the sine and cosine graphs, and the secant graph is an inverse of the cosine graph, the graph of sine can be used to construct the graph of the secant function
Mathematically:
since sec x = 1 / cos x
and, cos x = sin (90 - x)
therefore, sec x = 1 / sin (90 - x)
The graphs of the sine and secant functions are attached to this solution
Learn more here: brainly.com/question/9554579
