Help to Integral Calculus Solutions & Examples

Find parametric equations for the following curves. Include an interval for the parameter values.
 Answers are not unique.
A circle centered at (-2, -3) with radius 8, generated clockwise

Find an equation of the following curve in polar coordinates and describe the curve.         ${\displaystyle x=(1+\cos t)\cos t,y=(1+\cos t)\sin t.0\le t\le 2\pi }$

To solve:
${\displaystyle 3(x-1.1)=5x-5.3}$

To solve: The linear equation ${\displaystyle 0.2z=20}$

Provide the standard equations for lines and conic sections in polar coordinates with examples.

Graph the lines and conic sections ${\displaystyle r=4\sec (\theta +\frac{\pi }{6})}$

Evaluate the integral.
${\displaystyle \int \frac{x^5+3x^4}{x^2}dx}$

Evaluate the integral.
${\displaystyle {\int }_0^1\sin \left(3\pi t\right)dt}$

Pollen analysis, or palynology, is an important tool used in archaeology. Palynologists take samples of soil from archaeological sites and analyze the pollen from different soil layers. By examining the changes in pollen types over time, palynologists can learn about historical land use. The pollen in the soil indicates how the land was used—whether it was cultivated, a forest was cleared, or if it was abandoned. Scientists have been trying to find the origin of corn. They know that corn was domesticated from a plant called teosinte that grew somewhere in the central valley of Mexico between 12,000 and 6,000 years ago. It often is hard to find intact corncobs because they do not fossilize well. How could a palynologist help determine the origin of corn?

Evaluate each integral.
${\displaystyle \int {\cot h}^{2}x{\csc h}^{2}xdx}$

Find the indefinite integral.
${\displaystyle \int \cos 6xdx}$

Sketch the three basic conic sections in standard position with vertices and foci on the x-axis.

To convert the given radical expression to its rational exponent form and then simplify

To convert the given radical expression $\sqrt[4]{3^2}$ to its rational exponent form and then simplify

To convert the given radical expression ${\displaystyle \sqrt[4]{49}\sqrt{7}}$ to its rational exponent form and then simplify.

To determine: The radical form of ${\displaystyle x^2\sqrt{x}}$ in the rational exponent form.

To calculate : The domain of the expression $\sqrt[3]{x+7}$

Evaluate the indefinite integral.
${\displaystyle \int \sqrt{8-9t}dt}$

Evaluate the definite integral.
${\displaystyle \int \sin xdx}$

Evaluate the integrals.
${\displaystyle \int \cos 3xdx}$