Question

Physically, integrating ſ /(x)dx means finding the
(A) area under the curve from a to b
(B) area to the left of point a
(C) area to the right of point b
(D) area above the curve from a to b​

Answer 1

Answer:

hey mate here is your answer

Step-by-step explanation:

Given that the diagonal BD the diagonal AC in AO : OC in 3 : 1

To prove : AB = 3CD

Proof : in Δ AOC and Δ DOC

Δ AOB = Δ COD

Δ OBA = Δ ODC (Because DC is parallel to AB, and DB is transversal so these are alternates)

Therefore,

Δ AOB is similar to COD (By AA similarity)

Now, AO/OC = AB/DC (Because in similar triangles sides are proportional)

3/1 = AB/DC (Given that AO : OC = 3 : 1)

So, AB = 3DC

Hence proved.

hope it helps

Answer 2

Answer:

Step-by-step explanation:

Given that,

  $\int\limits^b_a {f(x)} \, dx$

we know that,

Integrating $\int\limits^b_a {f(x)} \, dx$

Means finding,

The area under the curve of the function $f(x)$ from a to b.

Let $y=f(x)$ be a function.

Then integration of $f(x)$  over interval [a, b]

It Represents area under the curve from a to b.

∴  $\int\limits^b_a {f(x)} \, dx$ = Area of the shaded region.

Answer: Option (A).

Integrating $\int\limits^b_a {f(x)} \, dx$ means area under the curve from a to b.

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