Class 12 Maths NCERT Solutions for Chapter 7 Integrals Exercise 7.8
![Class 12 Maths NCERT Solutions for Chapter 7 Integrals Exercise 7.8 Class 12 Maths NCERT Solutions for Chapter 7 Integrals Exercise 7.8](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT3zKj8VdjJVJYnqskW3oxBo29gYniHjsyAoiVDWlLigoinUfTMWdLNqSU03b_hey2yWQIeA6cMu21RHPEJWsLvhJos1dqjrytgcuJfAOE5erwUVaxzeyRWcVXQqgtuPFcz76xf95NyqrJI76o569h5fSCQZQDvSyZW8cJ5WaKPYj8TyZMxDQmA-dY/w650-h307-rw/cbse-class-12-maths-ncert-solutions-chapter-7-exercise-7-8.jpg)
Integrals Exercise 7.8 Solutions
1. Evaluate the following definite integrals as limit of sums.
∫ab x dx
Solution
It is known that,
2. Evaluate the following definite integrals as limit of sums.
∫ab (x + 1) dx
Solution
Let I = ∫ab (x + 1) dx
It is known that,
Here, a = 0, b = 5, and f(x) = (x + 1)
⇒ h = (5 - 0)/n = 5/n
3. ∫23 x2 dx
Solution
It is known that,
Here, a = 2, b = 3, and f(x) = x2
⇒ h = (3 - 2)/n = 1/n
4. ∫23 (x2 - x) dx
Solution
a = 1, b = 4, and f(x) = x2
∴ h = (4 - 1)/n = 3/n
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfco1h1QpxaHDRC-0ghnMb1NtdYKG1h8xRw6dGjoVcR-c-UXeEa9jrIiK0y4v34Dlz6_SVFXDctZ1ctfQ_hKymhov01sUYHsTE6g-spUZwn2JMDhBnjewWZXsXWg12dfxeBPMuIuMes9fLH37pNrnkzqiMX9N0LLXqXFPZ-EwzlUihkoxwWgHQJXMy/w515-h383-rw/NCERT%20Solutions%20for%20Chapter%207%20Integrals%20Class%2012%20Maths%20Exercise%20-%207.8%20img%207.JPG)
= 3[1 + 3 + 3]
= 3(7)
I1 = 21 ...(2)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6-PPYMJHAM_xv5FZ-vMsFqOKo8sSWMvDC8579I4ka9SwyTFQHxFrseiPfMrR3iwvvHaBfjX0jhNQXhDeXT0lJyt7_Acxl9JfXpTAMtLpyIt3-fbk8oTH7KfDJ3U-Fjf83L9MOR4iH-mdwws2enflJLOStyvFX1bu6BfKn1Y0TDIsWgG_EFJQr4Ccx/w119-h38-rw/NCERT%20Solutions%20for%20Chapter%207%20Integrals%20Class%2012%20Maths%20Exercise%20-%207.8%20img%208.JPG)
a = 1, b = 4, and f(x) = x
⇒ h = (4 -1)/n = 3/n
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhORVdbfEOExPIDmS_Gmd3QXshjkaGsJGXycEONIbqvSUmNXzgcr6i9DSkZVV4IMgEuV3wnHu5VlfDSChXS-cpcS87ZjzRHDokwZJ__4fwsDgTfTiDwy_P_MCa8bxZz_-hVMCMGvFXr1rp5sWmU3TLUSLU2GX7jaOod6cpPmmpb5c0do97-ClgSQM29/w366-h438-rw/NCERT%20Solutions%20for%20Chapter%207%20Integrals%20Class%2012%20Maths%20Exercise%20-%207.8%20img%209.JPG)
From equations (2) and (3), we obtain
∴ h = (4 - 1)/n = 3/n
= 3[1 + 3 + 3]
= 3(7)
I1 = 21 ...(2)
a = 1, b = 4, and f(x) = x
⇒ h = (4 -1)/n = 3/n
From equations (2) and (3), we obtain
I2 = 15/2 ...(3)
From equations (2) and (3), we obtain
From equations (2) and (3), we obtain
I = I1 + I2 = 21 - 15/2 = 27/2
5. Evaluate the following definite integrals as limit of sums ∫-11 ex dx
Solution
6. Evaluate the following definite integrals as limit of sums ∫04 (x + e2x ) dx
Solution
It is known that ,
Here, a = 0, b = 4, and f(x) = x + e2x
∴h = (4 - 0)/n = 4/n