Integrating Standard Functions
Muhtasari
Integration is differentiation in reverse: it recovers a function from its rate of change, and it measures areas under curves. As with derivatives, a short list of standard integrals does most of the work, with a neat adjustment for the linear expressions \(ax+b\) that appear inside them.
In this lesson you will integrate powers, sines, cosines and the exponential, including the cases \((ax+b)^n\), \(\sin(ax+b)\), \(\cos(ax+b)\) and \(e^{ax+b}\). You will always add the constant of integration \(+c\) for an indefinite integral, the detail examiners look for first.
Malengo
- Integrate functions of the form (ax + b) to the power n (for any rational n, including n = -1), sin(ax + b), cos(ax + b), sec^2(ax + b) and e to the power (ax + b).
- Include an arbitrary constant of integration for indefinite integrals.
Somo la Sauti
Sikiliza somo hili kwenye programu
Ramani ya mawazo
Mada hii imechorwa ili uone jinsi mawazo yanavyounganika.
Fungua ramani ya mawazo kwenye programu
Kadi za kumbukumbu
Mazoezi ya haraka ya kumbukumbu kuhusu kinachopimwa katika mada hii.
Fanya mazoezi ya kadi hizi kwenye programu
Maelezo ya Somo
Dokezo Kamili la Somo Linapatikana kwenye Programu ya Green Bridge
Pata programu ya Green Bridge CBT kwenye simu au kompyuta yako kwa maktaba kamili ya IGCSE: mitihani ya miaka iliyopita, miongozo ya usahihishaji, ramani za mawazo, kadi za marudio na masomo ya sauti.
Tathmini ya Somo
Hongera kwa kukamilisha somo la Integrating Standard Functions. Sasa kwa kuwa umechunguza dhana na mawazo muhimu, ni wakati wa kuweka ujuzi wako kwa mtihani. Sehemu hii inatoa mazoezi mbalimbali maswali yaliyoundwa ili kuimarisha uelewaji wako na kukusaidia kupima ufahamu wako wa nyenzo.
Utakutana na mchanganyiko wa aina mbalimbali za maswali, ikiwemo maswali ya kuchagua jibu sahihi, maswali ya majibu mafupi, na maswali ya insha. Kila swali limebuniwa kwa umakini ili kupima vipengele tofauti vya maarifa yako na ujuzi wa kufikiri kwa makini.
Tumia sehemu hii ya tathmini kama fursa ya kuimarisha uelewa wako wa mada na kubaini maeneo yoyote ambapo unaweza kuhitaji kusoma zaidi. Usikatishwe tamaa na changamoto zozote utakazokutana nazo; badala yake, zitazame kama fursa za kukua na kuboresha.
- What is the integral of x^4 with respect to x? A. 4x^3 + c B. x^5/5 + c C. x^5 + c D. x^3/3 + c Answer: B
- What is the integral of (2x + 1)^3 with respect to x? A. (2x + 1)^4/4 + c B. (2x + 1)^4/8 + c C. 3(2x + 1)^2 + c D. (2x + 1)^4 + c Answer: B
- What is the integral of cos(2x)? A. sin(2x) + c B. (1/2) sin(2x) + c C. -(1/2) sin(2x) + c D. 2 sin(2x) + c Answer: B
- What is the integral of e^{3x}? A. e^{3x} + c B. 3e^{3x} + c C. (1/3) e^{3x} + c D. e^{3x}/x + c Answer: C
- For an indefinite integral, you must always: A. divide by x B. add the constant + c C. multiply by 2 D. take a logarithm Answer: B
Fanyia kazi maswali haya kwenye programu
Fanyia kazi maswali haya kwenye programu
Vitabu Vinavyopendekezwa
Fanya Mazoezi ya Maswali ya Majaribio
Ungependa kufanya mazoezi ya maswali ya majaribio kuhusu Integrating Standard Functions? Pakua programu ya Green Bridge CBT ili kupata maswali ya majaribio na tathmini kamili za mazoezi kuhusu mada hii.
Pakua Programu Kwenye Google Playstore
Kila kitu unachohitaji ili kufaulu katika JAMB, WAEC & NECO.
