Definite Integrals And Areas
Gbogbo ọrọ náà
A definite integral evaluates an integral between two limits and gives a number: most usefully, the area under a curve between those limits. It turns the abstract idea of integration into concrete areas and totals.
In this lesson you will evaluate definite integrals and apply integration to the evaluation of plane areas.
Ebumnobi
- Evaluate definite integrals.
- Apply integration to the evaluation of plane areas.
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Maapụ uche
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Kaadị ncheta
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Akwụkwọ Ọmụmụ
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Nnyocha Ọmụmụ
Ekele diri gi maka imecha ihe karịrị na Definite Integrals And Areas. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- A definite integral from a to b equals: A. F(a) - F(b) B. F(b) - F(a) C. F(b) + F(a) D. F(b) x F(a) Answer: B
- Evaluate the integral of 3x^2 from 0 to 2. A. 4 B. 6 C. 8 D. 12 Answer: C
- A definite integral needs a constant of integration: A. yes, always B. no, it cancels C. only sometimes D. only if negative Answer: B
- The definite integral of a positive function gives: A. the gradient B. the area under the curve C. the turning point D. the root Answer: B
- If part of the curve is below the x-axis, the integral of that part is: A. positive B. negative C. zero D. undefined Answer: B
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