Question

approximate value of the area of the region y=4x^(2),y=e^(x)

249

likes

1246 views

Answer to a math question approximate value of the area of the region y=4x^(2),y=e^(x)

$Expert avatar$

Ali

4.4

92 Answers

Step-by-step solution:

1. Set

4x^2 = e^x

to find intersection points.

2. Solve for

using LambertW function:

x = -2\text{LambertW}(-\frac{1}{4})

and

x = -2\text{LambertW}(\frac{1}{4})

.

3. Determine that

4x^2

is on top in the interval between intersection points.

4. Set up the integral

A = \int_{-2\text{LambertW}(-\frac{1}{4})}^{-2\text{LambertW}(\frac{1}{4})} (4x^2 - e^x) \, dx

.

5. Integrate and evaluate at the limits.

6. Numerically calculate the area to get approximately

0.801

square units.

Frequently asked questions (FAQs)

What is the resultant displacement when a vector of magnitude 18 units, directed 30° east of north, is added to a vector of magnitude 24 units, directed 60° south of east?

Math question: What is the measure of angle BAC in a circle with diameter AC? (

What is the value of sine of π/3?

New questions in Mathematics

1 + 1

A college believes that 22% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 5 percentage points?

a) A tap can supply eight gallons of gasoline daily to each of its 250 customers for 60 days. By how many gallons should each customer's daily supply be reduced so that it can supply 50 more customers for twenty more days?

a bank finds that the balances in its savings accounts are normally distributed with a mean of $500 and a standard deviation off of $40. What is the probability that a randomly selected account has a balance of more than $400?

A consulting company charges a fee of $50 per hour for consulting. If their monthly fixed costs are $1,000 and they want to make a monthly profit of $2,500, how many consulting hours should they bill per month?

(6.2x10^3)(3x10^-6)

x/20*100

7273736363-8

A force of 750 pounds compresses a spring 3 inches from its natural length, which is 15 inches. What will be the work done to compress it 3 inches more?

Substitute a=2 and b=-3 and c=-4 to evaluate 2ac/(-2b^2-a)

1. A pediatric client is prescribed digoxin for congestive heart failure. The dose prescribed is 40 mcg/kg twice daily. The child weighs 33 pounds. What is the dosage in mg to be given per dose? Round to the nearest hundredth. Calculate your answer in mg per dose. Enter numerical value only.____mg

prove that for sets SS, AA, BB, and CC, where AA, BB, and CC are subsets of SS, the following equality holds: (A−B)−C=(A−C)−(B−C)

How do you convert a fraction to a decimal

answer this math question The scale on a map is drawn so that 5.5 inches corresponds to an actual distance of 225 miles. If two cities are 12.75 inches apart on the map, how many miles apart are they? (Round to the nearest tenth) miles apart. The two cities are how many miles apart

Find the orthogonal projection of a point A = (1, 2, -1) onto a line passing through the points Pi = (0, 1, 1) and P2 = (1, 2, 3).

8(x+4) -4=4x-1

Two trains leave stations 294 miles apart at the same time and travel toward each other. One train travels at 95 miles per hour while the other travels at 115 miles per hourHow long will it take for the two trains to meet?

If the area of a circle is 75.7ft2, what is the radius? Give the answer in metres. Round answer to 2 decimal places and enter the units.

x(squared) -8x=0

The domain of the function f(x)=x+7x2−144 is (−∞,), ( ,), and ( , ∞).

approximate value of the area of the region y=4x^(2),y=e^(x)

Answer to a math question approximate value of the area of the region y=4x^(2),y=e^(x)

You might be interested in