# Thread: Solve Integral with TI-84 Plus

1. ## Solve Integral with TI-84 Plus

It's been a long time since I've done any calculus, so I've forgotten how to use my calculator to solve integrals. I have to solve

$\int_1^x \! (1/t) \, \mathrm{d}t$

for a few different x values. How can I do this using a graphing calculator (TI-84 Plus)?

2. Originally Posted by kwikness
It's been a long time since I've done any calculus, so I've forgotten how to use my calculator to solve integrals. I have to solve

$\int_1^x \! (1/t) \, \mathrm{d}t$

for a few different x values. How can I do this using a graphing calculator (TI-84 Plus)?
You need a Ti - 89.

3. Originally Posted by dwsmith
You need a Ti - 89.
A TI-84+ is recommended for the course. Here is the problem out of the book:

4. Originally Posted by kwikness
A TI-84+ is recommended for the course. Here is the problem out of the book:
Unless they have changed those calculators, they can't integrate with respect to a variable. If you had and integral bounded by values not at an asymptote, you could graph it, hit calculate, select integrate, and put in the bounds.

5. Hi there, you are not required to evaluate that integral.

You need to make a table in the Ti-84 to solve the approximation of the intergal using simpson's rule.

Do you know what this rule is?

6. Originally Posted by pickslides
Hi there, you are not required to evaluate that integral.

You need to make a table in the Ti-84 to solve the approximation of the intergal using simpson's rule.

Do you know what this rule is?
I looked up Simpson's rule, but I'm not sure how to apply it to doing this problem with a calculator. Does anyone have any advice?

7. Originally Posted by kwikness
I looked up Simpson's rule,
Is this the rule?

$\displaystyle \int_a^b f(x)~dx \approx \frac{b-a}{6}\left[ f(a)+4f\left(\frac{b-a}{2}\right)+f(b)\right]$

If so you are given different upper bounds in the first row of the table.

For $x = 0.5$ then $\displaystyle \int_1^{0.5} f(x)~dx \approx \frac{0.5-1}{6}\left[ f(1)+4f\left(\frac{0.5-1}{2}\right)+f(1)\right]=\dots$

Using the calculator gives you the power to evaluate all these sums at the same time.

8. Originally Posted by pickslides
Is this the rule?

$\displaystyle \int_a^b f(x)~dx \approx \frac{b-a}{6}\left[ f(a)+4f\left(\frac{b-a}{2}\right)+f(b)\right]$

If so you are given different upper bounds in the first row of the table.

For $x = 0.5$ then $\displaystyle \int_1^{0.5} f(x)~dx \approx \frac{0.5-1}{6}\left[ f(1)+4f\left(\frac{0.5-1}{2}\right)+f(1)\right]=\dots$

Using the calculator gives you the power to evaluate all these sums at the same time.
That is Simpson's rule for $n=2$

The OP asked for Simpson's rule with $n=10$

In general we have

$n$ must be even and $\displaystyle \Delta x=\frac{b-a}{n}$

$x_i=a+i\Delta x, i=0,1,2,...,n$

$\displaystyle \int_{a}^{b}f(x)dx=\frac{\Delta x}{2}\left[ f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+...+2f(x_{n-2}+4f(x_{n-1})+f(x_n)\right]$

9. Originally Posted by TheEmptySet
That is Simpson's rule for $n=2$

$\displaystyle \int_{a}^{b}f(x)dx=\frac{\Delta x}{2}\left[ f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+...+2f(x_{n-2}+4f(x_{n-1})+f(x_n)\right]$

• How do I determine what to put in the denominator under delta x?
• How do I get past leaving a 0 in the denominator when I evaluate X of 0? $f(x_0) = 1/0$
• Also, I'm having trouble figuring out what the best way to evaluate this on a calculator would be. I have to evaluate it at .5, 1.5, ...

10. Simpson's rule to approximate the value of a definite integral ...

for $x = 0.5$ ...

$\Delta x=\dfrac{0.5-1}{10} = -.05$

$\displaystyle \int_{1}^{0.5} \frac{1}{t} \, dt \approx \frac{-0.05}{3}\left[ \frac{1}{1}+4 \cdot \frac{1}{.95} + 2 \cdot \frac{1}{.90} + 4 \cdot \frac{1}{.85} + 2 \cdot \frac{1}{.80} + 4 \cdot \frac{1}{.75} + 2 \cdot \frac{1}{.70} + 4 \cdot \frac{1}{.65} + 2 \cdot \frac{1}{.60} + 4 \cdot \frac{1}{.55} + \frac{1}{.50}\right] = -0.6931502307$

now do the same for every x-value (upper limit of integration) in the table.