Applications Of Calculus
Akopọ
Integration does far more than reverse differentiation. It lets you calculate the exact area enclosed by a curve, find the region trapped between two graphs, and even compute the volume of a solid formed by spinning a curve around an axis. These ideas turn abstract equations into concrete measurements.
You will also see how calculus drives kinematics: velocity is the derivative of displacement, and acceleration is the derivative of velocity. By integrating or differentiating, you can move freely between displacement, velocity and acceleration, solving motion problems that algebra alone cannot reach.
Awọn Afojusun
- Understand how displacement, velocity and acceleration are related using calculus
- Determine areas under curves and between curves using integration
- Determine volumes of revolution about the coordinate axes
Àwòrán ọpọlọ
A ti ṣe àwòrán kókó yìí kí o lè rí bí àwọn èrò ṣe so pọ̀.
Ṣí àwòrán ọpọlọ nínú áàpù
Káàdì ìrántí
Ìdánrawò kíákíá lórí ohun tí wọ́n ń dán wò nínú kókó yìí.
Ṣe ìdánrawò káàdì wọ̀nyí nínú áàpù
Akọ̀wé Ẹ̀kọ́
Àkọsílẹ̀ Ẹ̀kọ́ Pípé wà lórí Ohun Èlò Green Bridge
Gba ohun èlò Green Bridge CBT sórí fóònù tàbí kọ̀mpútà rẹ fún gbogbo ilé ìkàwé IGCSE: ìwé ìdánwò àtijọ́, ìlànà ìdíwọ̀n, àwòrán èrò, káàdì ìkẹ́kọ̀ọ́ àti ẹ̀kọ́ ohùn.
Ìdánwò Ẹ̀kọ́
Oriire fun ipari ẹkọ lori Applications Of Calculus. Ni bayi ti o ti ṣawari naa awọn imọran bọtini ati awọn imọran, o to akoko lati fi imọ rẹ si idanwo. Ẹka yii nfunni ni ọpọlọpọ awọn adaṣe awọn ibeere ti a ṣe lati fun oye rẹ lokun ati ṣe iranlọwọ fun ọ lati ṣe iwọn oye ohun elo naa.
Iwọ yoo pade adalu awọn iru ibeere, pẹlu awọn ibeere olumulo pupọ, awọn ibeere idahun kukuru, ati awọn ibeere iwe kikọ. Gbogbo ibeere kọọkan ni a ṣe pẹlu iṣaro lati ṣe ayẹwo awọn ẹya oriṣiriṣi ti imọ rẹ ati awọn ogbon ironu pataki.
Lo ise abala yii gege bi anfaani lati mu oye re lori koko-ọrọ naa lagbara ati lati ṣe idanimọ eyikeyi agbegbe ti o le nilo afikun ikẹkọ. Maṣe jẹ ki awọn italaya eyikeyi ti o ba pade da ọ lójú; dipo, wo wọn gẹgẹ bi awọn anfaani fun idagbasoke ati ilọsiwaju.
- What does the definite integral of y = f(x) between x = a and x = b represent geometrically? A) The gradient of the curve B) The signed area between the curve and the x-axis C) The volume of revolution D) The length of the curve Answer: B
- The region under y = 3x from x = 0 to x = 2 is rotated about the x-axis. What is the volume? A) 12 pi B) 24 pi C) 36 pi D) 6 pi Answer: C
- A particle has displacement s = t^3 - 6t^2 + 9t. When is it instantaneously at rest? A) t = 1 and t = 3 B) t = 0 and t = 3 C) t = 2 only D) t = 3 only Answer: A
- To find the area between two curves y = f(x) and y = g(x), you calculate: A) The integral of f(x) times g(x) B) The integral of f(x) + g(x) C) The integral of f(x) - g(x) where f is above g D) The integral of f(x) divided by g(x) Answer: C
- The volume of revolution about the x-axis formula uses: A) pi times the integral of y dx B) pi times the integral of y squared dx C) The integral of pi y dx D) 2 pi times the integral of y dx Answer: B
Ṣiṣẹ́ lórí àwọn ìbéèrè wọ̀nyí nínú ohun èlò náà
Ṣiṣẹ́ lórí àwọn ìbéèrè wọ̀nyí nínú ohun èlò náà
Awọn Iwe Itọsọna Ti a Gba Nimọran
Ẹ̀kọ́ síwájú láti àwọn orísun ṣíṣí
-
Abala ìwé ẹ̀kọ́
Derivatives
Find the derivative of a function.
"Precalculus: Derivatives" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/precalculus/pages/12-4-derivatives. Access for free at https://openstax.org/books/precalculus/pages/1-introduction
Àwọn àjọ mìíràn ló tẹ̀ wọ́n jáde lábẹ́ ìwé àṣẹ ṣíṣí, a sì dá wọn lọ́lá bí wọ́n ṣe béèrè. Àwọn ìjápọ̀ ń ṣí ojú òpó wọn.
Ṣe Adaṣe Awọn Ibeere Idanwo Adaṣe
Ṣe o fẹ ṣe adaṣe awọn ibeere idanwo adaṣe nipa Applications Of Calculus? Ṣe igbasilẹ ohun elo Green Bridge CBT lati wọle si awọn ibeere idanwo adaṣe ati awọn ayẹwo adaṣe kikun fun koko-ọrọ yii.
Ṣe igbasilẹ ohun elo naa lori Google Playstore
Gbogbo ohun ti o nilo lati ṣe dara julọ ninu JAMB, WAEC ati NECO.
