(P3T9Q) Arc Length [QUIZ]

$$\left[\ln\left|\sec\left(x\right)+\tan\left(x\right)\right|\right]_0^{\frac{\pi}{4}}$$

STEP 7:

Evaluate the antiderivative at the upper bound.

(write down the answer with three decimals without rounding)

USE RADIANS!

$$\left[\ln\left|\sec\left(x\right)+\tan\left(x\right)\right|\right]_0^{\frac{\pi}{4}}$$

STEP 8:

Evaluate the antiderivative at the lower bound.

(write down the answer with three decimals without rounding)

USE RADIANS!

$$\left[\ln\left|\sec\left(x\right)+\tan\left(x\right)\right|\right]_0^{\frac{\pi}{4}}$$

STEP 9:

FINAL ANWER

What you got from the upper minus that of the lower.

(write down the answer with three decimals without rounding)

USE RADIANS!

STEP 1:

Calculate the derivative of the function $$x^2-\frac{ln\left(x\right)}{8}$$ .

$$\int_1^{10}\sqrt[]{1+\left[2x-\frac{1}{8x}\right]^2}dx$$

STEP 2:

After substituting everything in the formula.

Simplify the expression $$\left[2x-\frac{1}{8x}\right]^2$$ .

Use binomial squared:

$$\left(a+b\right)^2=a^2+2ab+b^2$$

$$\int_1^{10}\sqrt[]{1+4x^2-\frac{1}{2}+\frac{1}{64x^2}}dx$$

STEP 3:

Keep on simplifying.

Simplify the expression $$1+4x^2-\frac{1}{2}+\frac{1}{64x^2}$$ .

$$\int_1^{10}\sqrt[]{4x^2+\frac{1}{2}+\frac{1}{64x^2}}dx$$

STEP 4:

Keep on simplifying.

Factorize $$4x^2+\frac{1}{2}+\frac{1}{64x^2}$$ .

Use binomial squared:

$$\left(a+b\right)^2=a^2+2ab+b^2$$

$$\int_1^{10}\sqrt[]{\left(2x+\frac{1}{8x}\right)^2}dx$$

STEP 5:

Keep on simplifying.

Simplify $$\sqrt[]{\left(2x+\frac{1}{8x}\right)^2}$$ .

$$\int_1^{10}2x+\frac{1}{8x}dx$$

STEP 6:

Calculate the antiderivative of $$2x+\frac{1}{8x}$$ .

$$\left[x^2+\frac{1}{8}\ln\left(x\right)\right]_1^{10}$$

STEP 7:

Evaluate the antiderivative at the upper bound.

(write down the answer with three decimals without rounding)

$$\left[x^2+\frac{1}{8}\ln\left(x\right)\right]_1^{10}$$

STEP 8:

Evaluate the antiderivative at the lower bound.

(write down the answer with three decimals without rounding)

$$\left[x^2+\frac{1}{8}\ln\left(x\right)\right]_1^{10}$$

STEP 9:

FINAL ANWER

What you got from the upper minus that of the lower.

(write down the answer with three decimals without rounding)