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تکمل کے طریقے

Written by Hassan Raza (Mathematics)

ای کیٹ · ریاضی · 5 سوالات

نام: ____________________   تاریخ: ____________

  1. What is the value of the integral of (2x + 3) dx from 0 to 1?

    • A 4
    • B 5
    • C 2
    • D 3

  2. What is the integral of e^(3x) dx?

    • A e^(x) / 3 + C
    • B e^(3x) + C
    • C e^(3x) / 3 + C
    • D 3 e^(3x) + C

  3. What is the integral of 1 / (1 + x²) dx?

    • A ln(1 + x²) + C
    • B 1 / x + C
    • C sin inverse of x + C
    • D tan inverse of x + C

  4. What is the area enclosed between y = x and y = x² from x = 0 to x = 1?

    • A 1/3
    • B 1/2
    • C 1/6
    • D 1/4

  5. What is the integral of 2x / (x² + 1) dx?

    • A ln(x² + 1) + C
    • B x² / (x² + 1) + C
    • C 1 / (x² + 1) + C
    • D 2 ln x + C

جوابی کلید

1. A, 2. C, 3. D, 4. C, 5. A

  1. The antiderivative is x² + 3x. At 1 it is 4, and at 0 it is 0, so the value is 4.

  2. Dividing by the derivative of the exponent, 3, gives e^(3x) / 3 + C.

  3. The derivative of the inverse tangent of x is 1 / (1 + x²).

  4. The area is the integral of (x - x²) from 0 to 1, which is 1/2 - 1/3 = 1/6.

  5. The numerator is the derivative of the denominator, so the integral is ln(x² + 1) + C.