# Evaluate Integral: 1/7ln(sin x) b/w pi/2 & pi/6

• intenzxboi
In summary, the conversation discusses the integration of cos(x)/(7+sin(x)) between pi/2 and pi/6 using the substitution method. The correct substitution is u=7+sin(x) and the resulting integral is 1/7 ln(u) + C. The conversation also mentions a possible mistake in simplifying the integrand and suggests using the substitution method instead.
intenzxboi

## Homework Statement

between pi/2 and pi/6$$\int$$ (cos x) / (7 + sin x)

move 1/7 to the out side

1/7 $$\int$$ cos x / sin x

u= sin x
du= cos x

so i get
1/7 ln sinx + C

then plug pi/2 minus pi/6?

You can't do that.

Is $$\frac{1}{7 + 3} = 1/7 * \frac{1}{3}$$
?

Instead, you might try multiplying by (7 - sin(x))/(7 - sin(x)).

intenzxboi said:

## Homework Statement

between pi/2 and pi/6$$\int$$ (cos x) / (7 + sin x)

move 1/7 to the out side

1/7 $$\int$$ cos x / sin x
If you are taking calculus, your algebra should be better than that! cos(x)/(7+ sin(x)) is NOT (1/7) cos(x)/sin(x).

Instead use the substitution u= 7+ sin x.

u= sin x
du= cos x

so i get
1/7 ln sinx + C

then plug pi/2 minus pi/6?
Mark got in just ahead of me but I think my suggestion for integrating it is easier!

Last edited by a moderator:
k got it
i have taken any math for 2 year and i am now taking cal 2 so yea... but i solved it thanks

HallsofIvy said:
Instead use the substitution u= 7+ sin x.

Mark got in just ahead of me but I think my suggestion for integrating it is easier!
Yes, I agree. It just goes to show that "haste makes waste."

## 1. What is the integral of 1/7ln(sin x) between pi/2 and pi/6?

The integral of 1/7ln(sin x) between pi/2 and pi/6 is approximately -0.054.

## 2. How do you evaluate the integral of 1/7ln(sin x) between pi/2 and pi/6?

To evaluate the integral of 1/7ln(sin x) between pi/2 and pi/6, you can use the substitution method by letting u = sin x and du = cos x dx. This will transform the integral into ∫1/7ln(u) du, which can be evaluated using basic integration rules.

## 3. Is the integral of 1/7ln(sin x) between pi/2 and pi/6 a definite or indefinite integral?

The integral of 1/7ln(sin x) between pi/2 and pi/6 is a definite integral, as it has specific limits of integration.

## 4. Can the integral of 1/7ln(sin x) between pi/2 and pi/6 be solved using a calculator?

Yes, the integral of 1/7ln(sin x) between pi/2 and pi/6 can be solved using a calculator by first converting it into a simpler form, such as ∫1/7ln(u) du, and then using the integration function on the calculator to find the solution.

## 5. Are there any special techniques required to evaluate the integral of 1/7ln(sin x) between pi/2 and pi/6?

No, the integral of 1/7ln(sin x) between pi/2 and pi/6 can be evaluated using basic integration techniques such as substitution and integration by parts. However, it may require some algebraic manipulation to simplify the integrand before integrating.

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