Help me with this jus look at it and pls answer

kondor19780726 [428]

Answer:

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3 years ago

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The length of each side of a square is 3 inches more than the length of each side of a smaller square the sum of the areas of th

Svetradugi [14.3K]

The length of each side of a square is 3 in. more than the length of each side of a smaller square. The sum of the areas of the squares is 149 in. $^{2} .$ Find the lengths of the sides of the two squares.

4 0

3 years ago

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: $\displaystyle A = 10$