Integral Calculator Integral Calculator calculates an indefinite integral that is anti-derivative of a function with respect to a given variable. Online Integral Calculator is a tool which makes calculations easy and fun. It is used to integrate the given function with respect to the given variable. Try our Integral Calculator and get your problems solved instantly. Step by Step Calculations Step 1 : Observe the given function. Step 2 : Find the integration of the given function and add a integral constant(C) at the end. Example Problems Find integration for the function: f(x) = 3x4 + 2x3 + 7x + 12 Know More About Fraction To Decimal Converter
Step 1 : Given function: f(x) = 3x4 + 2x3 + 7x + 12 Step 2 : ∫(3x4+2x3+7x+12) dx = 3 ∫(x4) dx + 2 ∫(x3) dx + 7 ∫(x) dx + 12 ∫(1) dx = 3x55 + 2x44 + 7x22 + 12x = 3x55 + x42 + 7x22 + 12x + C Answer : 3x55 + x42 + 7x22 + 12x + C Find antiderivative for the function: f(x) = cos 8x? Step 1 : Given function: f(x) = cos 8x Step 2 : = ∫cos8x dx = sin(8x)8 = sin(8x)8 + C Answer : sin(8x)8 + C
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Quadratic Formula Calculator A Quadratic Equation is a second degree polynomial equation which is in the form: Ax2 + Bx + C = 0. Online Quadratic Formula Calculator is a tool which makes calculations easy and fun. It is used to solve the quadratic equation using the quadratic formula. Try our Quadratic Formula Calculator and get your problems solved instantly. Step by Step Calculations Step 1 : Observe the values of A(coefficient of x2), B(coefficient of x) and C(constant) as a, b and c. Step 2 : Find the value of discriminant(D) by using the formula (D) = b2 - 4ac. Step 3 : Check the value of discriminant(D). ⇒ If D > 0, then the equation has two real solutions given by: x1 = (−b)+D√2a and x2 =(−b)−D√2a
⇒ If D = 0, then the equation has two real solutions given by: x1 = (−b)2a and x2 =(−b)2a ⇒ If D < 0, then the equation has imaginary roots. Example Problems Solve x2 + 5x + 7 = 0. Step 1 : Given equation : x2 + 5x + 4 = 0 So, A(coefficient of x2) = 1 B(coefficient of x) = 5 C(constant) = 4 Step 2 : Now, discriminant(D)= b2 - 4ac D= 52 - 4(1)(4) D= 25 - 16 D= 9 Step 3 : Since D > 0, the equation has two real solutions given by. x1 = (−b)+D√2a = (−5)+9√2×1 = −22 = -1 x2 = (−b)−D√2a = (−5)−9√2×1 = −82 = -4
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Answer : x1 = -1 and x2 = -4 Solve x2 + 2x - 8 = 0. Step 1 : Given equation : x2 + 2x - 8 = 0 So, A(coefficient of x2) = 1 B(coefficient of x) = 2 C(constant) = -8 Step 2 : Now, discriminant(D)= b2 - 4ac D= 22 - 4(1)(-8) D= 4 + 32 D= 36 Step 3 : Since D > 0, the equation has two real solutions given by. x1 = (−b)+D√2a = (−2)+36√2×1 = 42 = 2 x2 = (−b)−D√2a = (−2)−36√2×1 = −82 = -4 Answer : x1 = 2 and x2 = -4
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