grislingatb

2021-11-23

Solve the integral.

${\int}_{1}^{9}{t}^{-\frac{1}{2}}dt$

Drood1980

Beginner2021-11-24Added 16 answers

Step 1

To find:

The definite integral of${\int}_{1}^{9}{t}^{-\frac{1}{2}}dt$ .

Formula used:

Power rule of integration:

$\left({x}^{n}\right)}^{\prime}=n{x}^{n-1$

Calculation:

The definite integral of${\int}_{1}^{9}{t}^{-\frac{1}{2}}dt$ can be obtained as,

$\int}_{1}^{9}{t}^{-\frac{1}{2}}dt={\left[\frac{{t}^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}\right]}_{1}^{9$

$=2{\left[\sqrt{t}\right]}_{1}^{9}$

$=2[\sqrt{9}-\sqrt{1}]$

=4

Step 2

Thus, the integral of${\int}_{1}^{9}{t}^{-\frac{1}{2}}dt$ is 4.

To find:

The definite integral of

Formula used:

Power rule of integration:

Calculation:

The definite integral of

=4

Step 2

Thus, the integral of

Kathleen Ashton

Beginner2021-11-25Added 15 answers

Step 1: Use Negative Power Rule: $x}^{-a}=\frac{1}{{x}^{a}$ .

${\int}_{1}^{9}\frac{1}{\sqrt{t}}dt$

Step 2: If f(x) is a continuous function from a to b, and if F(x) is its integral, then:

${\int}_{a}^{b}f\left(x\right)dx=F\left(x\right){\mid}_{a}^{b}=F\left(b\right)-F\left(a\right)$

Step 3: In this case,$f\left(t\right)=\frac{1}{\sqrt{t}}$ . Find its integral.

$2\sqrt{t}{\mid}_{1}^{9}$

Step 4: Since$F\left(t\right){\mid}_{a}^{b}=F\left(b\right)-F\left(a\right)$ , expand the above into F(9)−F(1):

$2\sqrt{9}-2\sqrt{1}$

Step 5: Simplify.

4

Step 2: If f(x) is a continuous function from a to b, and if F(x) is its integral, then:

Step 3: In this case,

Step 4: Since

Step 5: Simplify.

4

What is the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1)?

How to expand and simplify $2(3x+4)-3(4x-5)$?

Find an equation equivalent to ${x}^{2}-{y}^{2}=4$ in polar coordinates.

How to graph $r=5\mathrm{sin}\theta$?

How to find the length of a curve in calculus?

When two straight lines are parallel their slopes are equal.

A)True;

B)FalseIntegration of 1/sinx-sin2x dx

Converting percentage into a decimal. $8.5\%$

Arrange the following in the correct order of increasing density.

Air

Oil

Water

BrickWhat is the exact length of the spiraling polar curve $r=5{e}^{2\theta}$ from 0 to $2\pi$?

What is $\frac{\sqrt{7}}{\sqrt{11}}$ in simplest radical form?

What is the slope of the tangent line of $r=-2\mathrm{sin}\left(3\theta \right)-12\mathrm{cos}\left(\frac{\theta}{2}\right)$ at $\theta =\frac{-\pi}{3}$?

How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

Use the summation formulas to rewrite the expression $\Sigma \frac{2i+1}{{n}^{2}}$ as i=1 to n without the summation notation and then use the result to find the sum for n=10, 100, 1000, and 10000.

How to calculate the right hand and left hand riemann sum using 4 sub intervals of f(x)= 3x on the interval [1,5]?