Find the total surface area.

Determine the area enclosed by y=2x+3, the x-axis and the ordinates x=3 and x=4

jok3333 [9.3K]

Answer:

$\displaystyle \int\limits^4_3 {2x + 3} \, dx = 10$

General Formulas and Concepts:
Calculus

Integration

Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Area of a Region Formula: $\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx$

Step-by-step explanation:

Step 1: Define

Identify.

y = 2x + 3

x-interval [3, 4]

x-axis

See attachment for graph.

Step 2: Find Area

Substitute in variables [Area of a Region Formula]: $\displaystyle A = \int\limits^4_3 {2x + 3} \, dx$
[Integral] Rewrite [Integration Property - Addition/Subtraction]: $\displaystyle A = \int\limits^4_3 {2x} \, dx + \int\limits^4_3 {3} \, dx$
[Integrals] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle A = 2 \int\limits^4_3 {x} \, dx + 3 \int\limits^4_3 {} \, dx$
[Integrals] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle A = 2 \bigg( \frac{x^2}{2} \bigg) \bigg| \limits^4_3 + 3(x) \bigg| \limits^4_3$
[Integrals] Integrate [Integration Rule - FTC 1]: $\displaystyle A = 2 \bigg( \frac{7}{2} \bigg) + 3(1)$
Simplify: $\displaystyle A = 10$

∴ the area bounded by the region y = 2x + 3, x-axis, and the coordinates x = 3 and x = 4 is equal to 10.

---

Learn more about integration: brainly.com/question/26401241

Learn more about calculus: brainly.com/question/20197752

---

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

3 0

2 years ago

Can you prove this congruent? Using what theorem/postulate?

slavikrds [6]

I'd say that, if the angles S and U are equal, as the SV and UV segments move towards each other, they meet at vertex V, the angles they make, angle SVT and UVT, have to be equal, because the side TV is shared by both, and has the same direction.

now, side TV is on both triangles, and is shared by both, so is the same length, so TV on one triangle is equal to TV on the other

check the picture below

so, you have one Angle, another Angle, and then a Side
A A S

3 0

3 years ago

Anastasia is grocery shopping with her father and wonders how much shopping is left to do. "We already have 6 0 % 60%60, percent

Molodets [167]

If there are 12 items adding up to 60%, we want to know how many items more it will take to equal 100% So set up this equation 12/x = .6 then solve for x. x=12/.6 x = 20 now that we know the total you can subtract 12 from 20 and get 8, that is the number of items left on the list.

8 0

4 years ago

Read 2 more answers

F

Aleks04 [339]

Answer:

F= 40

Step-by-step explanation:

F=ka

25 = k 5

k = 5

F=5a

F=5*8

F= 40

8 0

3 years ago

Which fraction correctly shows the probability of14 favorable outcomes and 37 possible outcomes?

zepelin [54]

Answer: 14/37

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers