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Solve math problem picture, — Step 1: Apply the Power Rule for Integration The power rule states that ∫xⁿ dx = xⁿ⁺¹/n+1 + C. For a sum of terms, integrate each

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Student question: "Find the integral of (x² + 3x) dx from 0 to 2."
Step 1: Apply the Power Rule for Integration
The power rule states that ∫xⁿ dx = (xⁿ⁺¹)/(n+1) + C. For a sum of terms, integrate each term separately.
Step 2: Integrate Each Term
∫x² dx = x³/3
∫3x dx = 3 * (x²/2)
So, the indefinite integral is (x³/3) + (3x²/2) + C.
Step 3: Apply the Limits of Integration (Definite Integral)
Evaluate the integral at the upper limit (2) and subtract its value at the lower limit (0).
[(2)³/3 + 3(2)²/2] - [(0)³/3 + 3(0)²/2]
= [8/3 + 3(4)/2] - [0 + 0]
= [8/3 + 12/2]
= [8/3 + 6]
= [8/3 + 18/3]
= 26/3
Final Answer:
The integral of (x² + 3x) dx from 0 to 2 is 26/3.

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A 2022 report by the National Achievement Survey (NAS) indicated that the average performance of Class 10 students in Mathematics was 32%. [NCERT, 2022]

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Zolver.in vs Other Study Methods

MethodWhat You GetTime to AnswerCost
Zolver.inStep-by-step AI explanation, organized notesInstantFree
Coaching ClassesTeacher explanation, limited personal attentionHours/DaysHigh
YouTubeVideo tutorials, often not specific to your QMinutesFree (with ads)
NCERT TextbookTheory, exercises, no instant doubt solvingDaysLow
WhatsApp GroupsPeer help, inconsistent quality, delayedMinutes/HoursFree

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Frequently Asked Questions

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